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UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE

AN INVESTIGATION OF MEANINGFUL UNDERSTANDING AND EFFECTIVENESS OF THE IMPLEMENTATION OF PIAGETIAN AND AUSUBELIAN THEORIES IN PHYSICS INSTRUCTION

A Dissertation SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of Doctor of Philosophy

By KAREN ANN WILLIAMS Norman, Oklahoma 1998

UMI Number: 9822813

UMI Microform 9822813 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

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300 North Zeeh Road Ann Arbor, MI 48103

© Copyright by KAREN ANN WILLIAMS 1998 All rights reserved.

AN INVESTIGATION OF MEANINGFUL UNDERSTANDING AND EFFECTIVENESS OF THE IMPLEMENTATION OF PIAGETIAN AND AUSUBELIAN THEORIES IN PHYSICS INSTRUCTION

A Dissertation APPROVED FOR THE DEPARTMENT OF INSTRUCTIONAL LEADERSHIP AND ACADEMIC CURRICULUM

BY

ACKNOWLEDGEMENTS It was with the help of others th a t this work was accomplished. I would like to acknowledge Dr. M arek for the tireless hours of reading revisions. Without the encouragement of Dr. M arek, I would have given up long ago and without the speediness of his turnaround time I never would have met deadlines. I would like to th an k the members of my committee for fighting for me when I needed them. Besides the knowledge from their classes. Dr. McKinney and Dr. Cavallo offered an understanding ear on more th an several occasions and provided encouragement. Dr. Stafford, the first person to introduce me to the learning cycle, taught me a way of teaching th a t was exactly the way th a t I learned. T hat made me th in k about this field of research rather th an doing more spectroscopic research which wouldn’t help my teaching in any g reat way. Dr. G rasse and his wife P a tt have been tremendous helps to me during my entire tim e a t OU. I would like to th an k my family and fnends for my “preoccupiedness” and absence from family/friend events because I h ad to do projects or papers. From the beginning my parents gave me the freedom to pursue any field of study. Without their powers of pursuasion, I probably would not have considered graduate school or teaching as a career. W ithout the support of the physics departm ent a t ECU this degree would not have become a reality. Scheduling courses changes so th a t I could attend classes and do research was done on many occasions. And last, b ut certainly not least, my heavenly F ather deserves credit. Luke 1:37 tells us th a t nothing is impossible with God. I would be lying if I said th a t He didn’t deserve a "lion’s share” of the credit. For I feel th a t He placed m any of the persons mentioned above in my path to help me achieve this goal. iv

TABLE OF CONTENTS List of Tables.................................................................................................... vil List of Figures...................................................................................................viii A bstract

«...................................................................................................... ix

Chapter 1: Introduction.................................................................................. 1 Background.............................................................................................. I Purpose of Study....................................................................................6 Significance of Study............................................................................. 6 Problem S tatem ent................................................................................ 8 Research Q uestions................................................................................9 Chapter 2: L iterature Review........................................................................ 10 Ausubelian Theory and Meaningfiil Learning...................................... 10 Meaningful Verbal Reception Learning................................................ 13 Research in Meaningful Learning.........................................................16 Piagetian Theory.....................................................................................33 Research in Piagetian Theory-Piagedan Stage Studies.................... 36 Lawson’s Modified Version of Piagetian Stage Theory.......................37 The Learning Cycle................................................................................ 39 The Learning Cycle and Similarities of Piagetian Theory to Ausubelian Theory........................................................................ 40 Learning Cycle Research.......................................................................41 Chapter 3; Methodology...................................................................................52 Design........................................................................................................52 Sample...................................................................................................... 52 Instructional T reatm ents...................................................................... 53 Variables and D ata Analysis.................................................................54 M easures.................................................................................................. 58 Chapter 4: Results...........................................................................................63 Question 1.................................................................................................63 Question 2.................................................................................................66 Question 3................................................................................................. 7 0 Question 4................................................................................................. 71

Chapter 5: Discussion/Conclusions............................................................... 75 Question 1.................................................................................................. 75 Question 2.................................................................................................. 82 Question 3.................................................................................................. 85 Question 4.................................................................................................. 86 Reference............................................................................................................89 Appendices Index...............................................................................................99 Appendix A: Perm ission Letter...................................................................... 100 Appendix B: In stru m en ts................................................................................. 102 Appendix C: L earning Cycles........................................................................... 135 Appendix D: MVRL Concept Maps................................................................. 195 Appendix E: Miscellaneous Statistics............................................................208

VI

LIST OF TABLES Table 1; Force D ata ANCOVA........................................................................ 63 Table 2: Density/Archimedes’ Principle D ata ANCDVA............................. 64 Table 3: H eat D ata ANCOVA......................................................................... 64 Table 4: Force D ata ANCOVA........................................................................ 64 Table 5: Density D ata ANCOVA.................................................................... 64 Table 6: H eat D ata ANCOVA......................................................................... 64 Table 7: ANCOVAS from Force D ata (specific understanding)................. 67 Table 8: ANCOVAS from Density/Archimedes’ Principle D ata (specific). 6 7 Table 9: ANCOVAS from H eat D ata (specific understanding).................. 68 Table 10: ANCOVA Adjusted M eans............................................................. 209 Table II: Pearson Correlation M atrix for Force D ata.................................210 Table 12: Pearson Correlation M atrix for Density/Archimedes’ D ata

211

Table 13: Pearson Correlation M atrix for H eat D ata..................................212 Table 14: Descriptive S tatistics for Force D ata...........................................213 Table 15: Descriptive Statistics for Density/Archimedes’ D ata................ 214 Table 16: Descriptive S tatistics for H eat D ata............................................215

vu

LIST OF FIGURES Figure 1: Energy Concept M ap...................................................................... 196 Figure 2: M atter Concept M ap.......................................................................197 Figure 3: H eat Concept M ap.......................................................................... 198 Figure 4: H eat Concept M ap (student)......................................................... 199 Figure 5: H eat Concept M ap (student)......................................................... 200 Figure 6: Newton’s Laws Problem Solving Concept Map........................... 201 Figure 7: Problem Solving using Energy Concept Map............................... 202 Figure 8: Problem Solving (with friction) using Energy Concept Map

202

Figure 9: M atter, Density, P ressure Concept Map......................................203 Figure 10: M atter, Density, Pressure Concept Map (student)...................204 Figure 11: M atter, Density, Pressure Concept Map (student).................. 205 Figure 12: Archimedes’ Principle Concept Map............................................206 Figure 13: Falling Object Concept M ap.........................................................207 Figure 14: Learning Cycle and Piagetian and Ausubelian Explanations... 7 7 Figure 15: MVRL and Piagetian and Ausubelian Explanations.................79

vm

ABSTRACT

One section of college students (N= 25) enrolled in an algebra-based physics course was selected for a Piagetian-based learning cycle (LC) treatm ent while a second section (N=25) studied in an Ausubelian-based meaningful verbal reception learning treatm ent (MVRL). This study examined th e students’ overall (concept + problem solving + mental model) meaningful understanding of force, densify/Archimedes Principle, and heat. Also examined were students’ meaningful understanding as measured hy conceptual questions, problems, and mental models. In addition, students’ learning orientations were examined. There were no significant posttest differences between the LC and MVRL groups for students’ meaningful understanding or learning orientation. Piagetian and Ausubelian theories explain meaningful understanding for each treatm ent. Students from each treatm ent increased their meaningful understanding. However, neither group altered their learning orientation. The results of meaningful understanding as measured by conceptual questions, problem solving, and mental models were mixed. Differences were attributed to the weaknesses and strengths of each treatm ent. This research also examined four variables (treatm ent, reasoning ability, learning orientation, and prior knowledge) to find which best predicted students’ overall meaningful understanding of physics concepts. None of these variables wet e significant predictors a t the .05 level. However, when the same variables were used to predict students’ specific understanding (i.e. concept, problem solving, or mental model understanding), the results were mixed. For forces and density/Archimedes Piinciple, prior knowledge and ix

reasoning ability significantly predicted students’ conceptual understanding. For heat, however, reasoning ability was the only significant predictor of concept understanding. Reasoning ability and treatm en t were significant predictors of students’ problem solving for heat and forces. For density/Archimedes Principle, treatm ent was the only significant predictor of students’ problem solving. None of th e variables were significant predictors of mental model understanding. This research suggested th a t Piaget and Ausubel used different terminology to describe learning yet these theories are similar. F urther research is needed to validate this premise and validate the blending of the two theories.

CHAPTER 1 Introduction Background of the Study Physics is a course dreaded by nearly all who are required to take it. Teachers also know th a t students gain little meaningful understanding from conventional physics instruction (McCloskey, Carmazza & Green, 1980; Moreira, 1977; Williams & Cavallo, 1995). Physics students often confess to memorizing material to get through courses (Williams & Cavallo, 1994). One possible reason for students’ tendency to memorize facts, equations, and laws and, consequently, to have a lack of understanding of physics is th a t the subject consists of m any abstract concepts (Inhelder & Piaget, 1958; Prosser, 1983; Linn, Clement, & Pulos, 1983). Students who do not possess the reasoning ability needed to deal w ith such concepts may resort to memorizing facts, formulas, and problem types to get through physics courses (Hammer, 1989; Hewett, 1995; Renner & Marek, 1988). Also, many physics teachers focus on formulas w ithout emphasizing the need for conceptual understanding of the subject. H ew ett (1995) states th a t “students can learn to solve problems... w ithout the faintest gut feeling for the concepts th a t underlie them” (p. 85). Meaningful learning is defined as “the formation of viable relationships among ideas, concepts, and information” (Williams & Cavallo, 1995). In other words, students w ith a meaningful learning orientation attem pt to make connections between concepts. W hereas, students not possessing a meaningful learning orientation memorize facts or verbatim statem ents of ideas found in a text or said by the teacher (Novak, 1984). The latter are called “rote learners”. Learning orientation is not dichotomous, either rote or meaningful, but rather, m ay exist along a continuum between the rote and

meaningful extremes. Meaningful understanding is the product th a t may result when a person with a meaningful learning orientation and sufficient prior knowledge interacts with content th a t has the potential of being learned in a meaningful way (Novak, 1984). The U.S. D epartm ent of Education (McKinney, 1993) stresses the need to teach mathematics and science for understanding rath er than for absorbing facts. More recently, the National Science Teachers Association (NSTA, 1993) recommended th a t the most appropriate approach to teaching is a constructivist approach. The NSTA addressed the problem of the lack of meaningful learning in this statement: “th e typical U.S. science program discourages real learning not only in its overemphasis on facts, but in its very structure which inhibits students from making important connections between facts” (NSTA, 1993, p. 2). They fu rth er state th a t this roteness of learning deters many students from continuing to study the sciences. Others who make recommendations about teaching physics also emphasize teaching so th a t understanding results from instruction (Michels, Sears, Verbrugge, & Palmer, 1957; Dickie, 1994; Aldridge & Strassenburg, 1995). Aldridge and Strassenburg (1995) describe content standards for high school physics in term s of understanding the relationship of a concept to various other related concepts. Although not explicitly mentioned, meaningful learning was described in terms of understanding the relationships of various physics concepts to one another. Thus, meaningful learning and its product, meaningful understanding, are im portant outcomes of physics instruction. Instruction th a t promotes meaningful learning according to Ausubelian theory would promote meaningful understanding (Ausubel, 1963; Novak, 1984; Wandersee, 1988). For meaningful understanding to occur, physics concepts m ust be potentially meaningful to the students. In addition, students m ust possess sufficient prior knowledge about a concept

and a meaningful learning orientation for meaningful learning to occur (Pines & Novak, 1985). Furtherm ore, students m ust make connections between concepts, ideas, and knowledge. These are th e requirem ents th a t instruction aimed a t promoting meaningful learning m ust satisfy. The learning cycle is a teaching procedure which has been found to increase reasoning ability, concept understanding, and achievement (Lawson, Abraham, & Renner, 1989; Lawson, 1995), b u t w hat effect would a learning cycle have on students’ meaningful learning orientations and meaningful understandings? Since the learning cycle increases reasoning ability, concept understanding, and achievement, what relationships are there between these variables, meaningful learning orientation, and meaningful understanding? It seems reasonable th a t a teaching procedure which produces increased conceptual understanding might also produce meaningful understanding of concepts. Williams and Cavallo (1995) found students’ reasoning ability to be significantly related to meaningful learning orientation. Hence, it is possible th a t the learning cycle, which has been found to increase reasoning ability, could also increase students’ meaningful learning orientation. Students’ meaningfiil understanding of physics concepts could be increased if the learning cycle shifted the students’ learning orientation more toward th e meaningful end of the continuum. Thus, the learning cycle is an instructional procedure th a t might promote meaningful learning as defined by Novak (1984) and Ausubel (1963). Does a learning cycle treatm ent have an effect on students’ meaningful learning orientations and meaningfid understanding? In other words, does allowing students to: (1) experiment with m aterials to gather data, (2) construct a concept from those data, and (3) expand this idea or concept cause a change in a students’ meaningful learning orientation in physics or meaningful understanding of physics concepts? If so, are these shifts

significant? In this study, students’ meaningful understanding of physics will be determined from the students’ scores on three m easurem ent items: (1) questions about physics concepts th a t are categorized as being a t higher levels of Bloom’s taxonomy (comprehension, synthesis, and analysis); (2) solving physics problems, typically th e only method of assessm ent of stu d en t understanding in m any physics courses; and (3) m ental models in which students respond in writing to dem onstrate their meaningful understanding of a topic by their ability to successfully relate it to other item s in correct ways. If the learning cycle treatm ent improves meaningful learning, then a t least one of the three m easures m ust indicate higher average scores for the students in the learning cycle as a resu lt of the treatm en t used in this study. In meaningful verbal reception learning (MVRL), students are presented potentially meaningful m aterial. In other words, the content is not to be discovered or invented by th e learner; it m ust be non-arbitrarily incorporated by tbe students into th eir cognitive structure. Thus, by being related to items in cognitive structure, th e content is m ade available for future use (Ausubel, 1963; Novak, 1984). Hence by design, MVRL is not rote in nature, and students engaged in meaningful verbal reception learning are not necessarily passive learners. MVRL was designed to be more efficient a t promoting meaningful understanding th a n discovery (Ausubel, 1963; Novak & Gowin, 1984; Novak, 1988a), b u t how does MVRL affect meaningful understanding of physics concepts? How does learning to incorporate content via MVRL affect students’ meaningful learning orientation and meaningful understanding of physics concepts? If MVRL does cause shifts in m eaningful orientation or understanding, w hat is th e magnitude of th e shifts? If such shifts are significant, MVRL should also promote improvements in meaningful understanding according to Ausubel (1963).

The learning cycle and MVRL treatm ents have been presented as possibly having an efifect on students’ meaningful learning orientation and meaningful understanding. The two treatm ents will be compared to determine if one treatm ent has a greater influence upon students’ meaningful learning orientation and meaningful understanding of physics concepts. It has been hypothesized th a t the learning cycle and MVRL treatm ents positively affect meaningful learning orientation, and thus, meaningful understanding. Could there be variables other th an meaningful learning orientation th a t contribute to a student’s meaningful understanding of physics? Reasoning ability bas been mentioned as a predictor of students’ meaningful understanding of physics concepts. Williams and Cavallo (1995) found th a t reasoning ability, and not meaningful learning orientation, was a statistically significant predictor of physics understanding as m easured by the FCI. Cavallo and Schafer (1994) found th a t meaningful learning orientation was the best predictor of meaningful understanding of genetics topics on all but one m easure for which prior knowledge was a better predictor. Ausubel claimed th a t prior knowledge was necessary for meaningful understanding; thus, prior knowledge should be examined as a predictor for meaningful understanding of physics concepts. This research will also examine the effect th a t instructional treatm ent has upon meaningful understanding. These questions will also be investigated in this study. Of the variables hypothesized to be useful predictors of students’ meaningful learning, which variable is more im portant for students’ meaningful understanding of physics concepts? Does students’ reasoning ability, their meaningful learning orientation, their prior physics knowledge, or their instructional treatm en t better predict students’ meaningful understanding of physics concepts?

Purpose o f the Study The purpose of this study is to determ ine if a learning cycle style physics class and a MVRL style physics class have any effects on students’ meaningful learning orientation and meaningful understanding of physics concepts. If so, in w hat direction are th e effects, and are th e effects significant? The two treatm ents will th en be compared to determ ine if one style causes significantly more students to increase their tendency to learn meaningfully and to have increased meaningful understanding of physics concepts. In addition, any effects due to instruction th a t exist on each submeasm e of meaningful understanding of physics as well as for overall meaningful understanding of physics will be examined. W hat other variables may predict students’ meaningfid understanding of physics concepts? Reasoning ability, meaningfiil learning orientation, prior knowledge, and instructional treatm ent will be examined to determine their power to predict students’ meaningfid understanding of physics concepts. Significance of the Studv No reported research has examined the use of the learning cycle to alter students’ meaningfid learning orientation or students’ meaningfid understanding of physics concepts. S tudents m ay need to be instructed in a way th a t promotes the abandonment of rote learning in favor of more meaningfid learning approaches. When this occurs according to Ausubel, more meaningfid understanding of physics concepts should occur. As has been stated earlier, students’ tendency to leam more and more meaningfidly and with more meaningfid understanding are desired outcomes of physics education. Thus, this study is significant to physics educators interested in improving students’ meaningfid understanding. Why was the learning cycle treatm en t chosen since it has not been examined w ith respect to meaningfid learning? Williams and Cavallo (1995)

found th a t students’ reasoning ability was significantly positively correlated to their meaningful learning orientation, and according to Lawson (1995) learning cycle instruction has been found to increase students’ reasoning ability. Based upon these findings, it seems possible th a t the learning cycle may promote an increased meaningful learning orientation, and consequently, more meaningful understanding of physics concepts by students. If learning cycle instruction increases reasoning ability, then perhaps, meaningful learning orientation is increased in a sim ilar manner. Thus, this research will provide information about the effects of th e learning cycle on meaningful learning. Why w as meaningful verbal reception learning chosen as a treatm ent? MVRL, as espoused by Ausubel (1963) and further modernized through the use of aids (concept maps and Vee diagrams) by Novak and Gowin (1984), was designed to be an efficient way for students to leam meaningfully. MVRL is often confused with traditional lecture instruction. However, the order of the presentation of m aterial in MVRL differs fi-om th a t of traditional lectures. In traditional lectures, m aterial is presented as homogeneous topics. Topics are typically taught in the order th a t th e chapters are presented because the topics are related, not because they are more general or inclusive th a n another topic. In MVRL, m aterial is presented so th a t the most general topics are presented first, then the more detailed and specific concepts are related to the more general ones. According to Ausubelian theory, meaningful learning m ust begin with the more general topics th a t provide th e scaffolding for the more specific ones presented later. If MVRL produces increased meaningful understanding with students in college physics, it could be a more economical teaching procedure th a n the learning cycle since MVRL can w ithstand higher student-to-teacher ratios with fewer negative effects than learning cycle instruction. In addition.

MVRL style physics classes a t the college level could he tau g h t over the Internet as MVRL does not require laboratory m aterials and instructors to lead students to the concept. Before universities invest much time and money in th e design of such a course, the efficiency of MVRL to produce meaningful understanding m ust be examined. Ausubel said th a t having a meaningful learning orientation was necessary for meaningful understanding, h ut he did not elaborate on how students should a tta in such an orientation. For example, MVRL m ight not increase students’ meaningful learning orientation. Therefore, if MVRL does not produce an increase in students’ meaningful learning orientation, it may not he a procedure th a t universities should select. Having an increasingly meaningful learning orientation should result in meaningful understanding over time, while having an increasingly more rote orientation should result in less meaningful understanding over time. Using MVRL to increase students’ meaningful learning orientation has not been examined. This research will provide information about any effects of meaningful verbal reception learning on aspects of meaningful learning. Problem S tatem ent The m agnitude and the direction of m easurable differences in students’ meaningful learning orientation and their meaningful understanding of physics concepts as determ ined hy three separate m easures will be examined after treatm ents. These differences will he examined for a class of students w ith learning cycle instruction and for a class of students with meaningful verbal reception learning instruction. The study will determine which variable (students’ reasoning ability, their meaningful learning orientation, th e ir prior knowledge of physics concepts, or the instructional treatm ent) is th e better predictor of students’ meaningful understanding of physics concepts.

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Research Q uestions The study is designed to allow the investigation of the following research questions: 1. W hat are the magnitude and direction of measurable significant differences in meaningful learning orientation and meaningful understanding of physics concepts betw een students with learning cycle instruction and those with m eaningful verbal reception learning instruction? 2. W hat are the magnitude and direction of measurable significant differences in meaningful understanding of physics concepts measured by (1) conceptual questions, (2) problem-solving, and (3) m ental models between stu d en ts w ith the learning cycle and meaningful verbal reception learning instruction? 3. Which variable (reasoning ability, meaningful learning orientation, prior knowledge, or instructional treatm ent) is the best predictor of overall meaningful understanding of physics concepts? 4. Which variable (reasoning ability, meaningful learning orientation, prior knowledge, or instructional treatm ent) is the best predictor for each sub-measure of meaningful physics understanding?

CHAPTER 2 Literature Review Ausubelian Theory and Meaningful Leam itiy Learning, inquiry or reception, can be rote or meaningful. So what is it that distinguishes rote from meaningful learning? Rote learning is the "arbitrary, verbatim, non-substantive incorporation of new knowledge into cognitive structure” (Novak & Gowin, 1984, p. 167). Rote learners do not try to integrate new information with existing information, nor is their learning related to experience. Meaningful learning occurs if the learning task can be related in a “non-arbitrary, substantive fashion to w hat th e learner already knows, and if the learner adopts a corresponding learning se t to do so” (Ausubel, 1963, p. 18). The first requirement above stipulates th a t the task m ust be potentially meaningful or, in other words, th a t th e task content is such th a t it can be related to previous knowledge, concepts, or ideas. For example, the memorization of nonsense letters, words, syllables, or numbers would not be considered a meaningful learning task because any relationship to previous concepts would be arbitrary. The second requirem ent for meaningful learning dem ands th a t the learner adopt a learning set. A person has a meaningful learning set if he or she can "relate substantive aspects of new concepts, information, or situations to relevant components of existing cognitive structure in ways th a t make possible the incorporation of derivative, elaborative, correlative, supportive, qualifying or representational relationships” (Ausubel, 1963, p. 22). A rote learning set, on the other hand, is one in which the learner intends only to memorize. Hence, w hat is internalized remains discrete and isolated from other information because it is not related to other p arts of existing cognitive structure. Researchers (Cavallo & Schafer, 1994) have defined meaningful learning orientation as 10

the tendency to form relationships between ideas, information, and facts of science. A person m ay tend to le a m meaningfully and thus have a more meaningful learning set or orientation. Another person m ay tend to leam by rote, and thus, have a more rote learning orientation. Orientation or learning set is not dichotomous, either rote or meaningful, but rath er exists along a continuum between th e rote and th e meaningful extremes. Possessing a meaningful learning se t enables one to have a meaningful learning process, but does not ensure th a t meaningful learning will occur. As one moves toward the meaningful end of the continuum in a discipline, the conceptual structures become more like those of an expert in the discipline (Novak, 1988b). Ausubel uses th e adverb "potentially^ to emphasize th a t a ta sk cannot be meaningful, only potentially so. Being potentially meaningful requires that; (1) the m aterial be capable of being non-arbitrarily related as well as (2) the individual doing the learning can relate the concept to his or her own structures. Thus, the second criterion requires th a t the learn er possess relevant prior knowledge before th e task may be potentially meaningful. Hence, the term "potentially meaningful” brings with it two criteria th a t m ust exist for meaningful learning to occur. In summary, the conditions th a t Ausubel claimed m ust exist for meaningful learning are: (1) the learn er m ust have relevant prior knowledge, (2) th e tasks m ust have the potential to be learned meaningfully, and (3) the learner m ust adopt a meaningful learning set or orientation. A successful outcome, meaningful understanding or meaning, may or m ay not occur depending on the above conditions surrounding the learner and the task. The theory behind Ausubel’s position espousing verbal reception learning is based on several key concepts or processes: subsum ption, progressive differentiation, superordinate learning, and integrative 11

reconciliation. Subsumption is the process in which “new information often is relatable to and subsum able under more general, more inclusive concepts” (Novak & Gowin, 1984, p. 97). Novak (1988b) defined subsum ption as the “incorporation of new knowledge into a specifically existing concept or proposition” (p. 11). General concepts are superordinate to less inclusive or more specific concepts or propositions. T hat m aterial is subsum able in a “non-arbitrary, non-verbatim fashion accounts for its potential meaningfulness” (Ausubel, 1963, p. 25). If m aterial w as not subsumable, the material would be considered rote and not potentially meaningful. Subsumption provides th e “anchorage for new m aterial”. However, subsumption also h as an obliterative tendency. As a resu lt of being related to and included w ith other items, the specific items become more and more melded together or less dissociable. Thus, obliterative subsum ption may also result in forgetting if the m aterial becomes indissociable. So to be subsumed means possible meaningfulness for material as well as later forgetting due to the obliterative tendency of subsumption. In meaningful verbal reception learning, repetition or overlearning has been advocated to maximize learning and minimize forgetting. Progressive differentiation is the principle th a t “meaningful learning is a continuous process wherein new concepts gain greater m eaning as new relationships (propositional links) are acquired” (Novak & Gowin, 1984, p. 99). Concepts are continually being: modified, made more explicit, and made more inclusive as the learner perceives greater and greater differences between the concept and related concepts. As a result of progressive differentiation, preciseness of understanding, or meaning, increases. Superordinate learning refers to the process in which a more general new concept subsum es previous subsumers (Novak, 1984). “New concepts or propositions acquired th a t connect the meanings of two or more related, 12

less inclusive ideas” is called superordinate learning (Novak, 1988, p. 12). One's concept of learning must be adjusted. No longer must we th in k th a t learning is accompanied by a change in behavior, b u t rather, learning is observed by a change in the learner’s meaning of experience. Therefore, previously learned concepts are subsumed and th u s take on new meaning. They can have new or different relationships w ith one another through progressive differentiation and integrative reconciliation. Integrative reconciliation is the principle by which the learner “recognizes new relationships (concept linkages) between related sets of concepts or propositions” (Novak & Gowin, 1984, p. 103). Integrative reconciliation tends to break the isolation or compartmentalization of concepts as relationships are formed between various previously isolated concepts or ideas. Furthermore, they propose th a t often new prepositional linkages between concepts displace misconceptions because a misconception is often simply th e failure to integrate a particular concept. Meaningful Verbal Reception Leam iny How is MVRL implemented in the classroom? Ausubel proposed the use of “appropriately relevant and inclusive” advance organizers to allow for progressive differentiation and integrative reconciliation (Ausubel, 1963, p. 81). Research by Purdom and Kromrey (1992), Glover, Bullock, and Dietzer (1990), Novak and Musonda (1991), as well as th a t by Rubin and Tamir (1988) support th is claim by Ausubel. Rubin and Tamir (1988) state, “the function of advance organizers is to provide a bridge between th e existing cognitive structure of the learner and the new content they have to leam ” (p. 477). The organizers are called “advance organizers” in th at they are presented before the learning task. Research has shown th a t a short delay should occur between the reading of the advance organizer and th e reading of the assignment (Glover, Bullock, and Dietzer, 1990). Such organizers should 13

be more abstract and more generalized as well as more inclusive in order th a t they explain, integrate, and interrelate the material th a t follows. The organizers act as subsumers in th a t they (1) provide a general overview prior to the m aterial and (2) encompass th e content and relevant concepts in an eüîcient manner. Such ultimate organizers do not exist in the learner. Only less relevant and less inclusive ones exist since the learner cannot have such organization prior to learning. Ausuhel claimed th at organizers prevent the isolation of similar concepts and term s because organizers “mobilize all available concepts in cognitive stru ctu re th a t are relevant for and can play a subsuming role” (Ausubel, 1963, p. 82). Subsumers may be relatively large or m ay be poorly developed “depending on the frequency th a t meaningful learning occurs in conjimction w ith a given subsumer” (Moreira, 1977, p. 8). According to Ausubel, without advance organizers or subsumers to provide anchorage, one m ust resort to rote learning. He claimed much rote learning is caused by students being forced to leam details before they have sufficient subsumers available on which to anchor the new material. Pines and W est (1986) claim “the mtdorify of students leam to play the ‘school game’ of rote learning and regurgitation of curricular knowledge” when students’ spontaneous knowledge and formal knowledge do not match (p. 597). The im portant point to remember in delivering instruction th a t is consistent with Ausubelian theory is th a t one m ust begin w ith the most general and more inclusive concepts and then anchor more detailed and specific concepts to the more general ones (Ausubel, 1963; Trowbridge & Wandersee, 1994). According to Ausubel (1968, p. 152), “it is less difficult for hum an beings to grasp the difierentiated aspects of a previously-leamed, more inclusive whole than to formulate the inclusive whole from its previously-leamed differentiated p arts”. He states th a t it is rare for textbooks to be organized from the more general concepts to the more 14

specific. Rather, topics th a t are hom(^eneous are p u t into separate chapters or subchapters because they are related (Ausubel, 1963; Moreira, 1977). There is little o r no consideration for the concepts’ inclusiveness, generality, or level of abstraction when topics are arranged topically. Moreira (1977) outlined a second sem ester calculus-based physics course consistent with Ausubelian theory and MVRL. He recommended th a t the course begin with a general discussion of physics and physicists, the context of physics w hether it be classical or modem, th e role of concepts in physics, the key concepts of classical physics, and th en a general discussion of the concepts of force and field. These concepts become subsumers for other subsumers in th e learners’ cognitive structures and the new concepts to come. Forces such a s electrical or nuclear forces should be learned and related to one another only after the concept of force is already situated in cognitive structure. It is in this hierarchical way th a t meaningful learning takes place. Fisher and Lipson (1985) state th a t those who attem pt on a regular basis to integrate knowledge and resolve contradictions are “more proficient learners th an those who routinely compartmentalize information” (p. 51). They claim learning meaningfully fits the old adage: “the more we know, the more we realize how much we don’t know” (Fisher & Lipson, 1985, p. 52). Pines and West (1986) examined cases in which students compartmentalized knowledge. For example, when a student learned a topic in school th at contradicted his or her prior personal knowledge, th e student usually abandoned his or her personal knowledge and rotely repeated the school knowledge without reconciling the two. This is not meaningful learning. Meaningful learning only occurs when prior knowledge and formal (i.e., school) knowledge coexist. In physics, students’ misconceptions and th eir lack of understanding often occur, perhaps because of th is lack of knowledge 15

intertwinement. The association between A usubel’s key processes (subsumption, progressive differentiation, superordinate learning, integrative reconciliation, and th e use of advance organizers) an d learning should be evident. I t is in this theoretical framework th a t Ausubel embraces meaningful verbal reception learning. Any method or tool th a t increases the use of these processes increases meaningful learning. Using these tools and advance organizers as well as implying a careful adherence to Ausubel’s th ree criteria for meaningful learning provide for meaningful verbal reception learning. Research in M ean in y fiil L e n m in y Research on various aspects of meaningful learning will be summarized and categorized into five areas: (1) studies finding rote learning orientations or lack of meaningful learning; (2) studies finding increases in meaningfiil learning; (3) studies relating meaningful learning orientation or meaningful understanding to other variables; (4) studies on concept m aps or Vee diagrams; and (5) studies about other tools or techniques th a t m ay bring about an increase in meaningful learning orientation, help students acquire meamngful understanding, or improve meaningful learning. Studies Illustrating Rote Leaminig/lÂttle M eaningfiil T ^am iny Research in meaningful verbal learning shows th a t many college-age students leam science content, concepts, and ideas by rote (Dickie,1994; Edmondson & Novak, 1993; Novak, 1988a; Williams & Cavallo, 1994). I t is reported th a t meaningful learning potential is undeveloped in our students (Novak & Musonda, 1991). Novak (1988a) stated th a t “the small am ount of science th a t is tau g h t in most elem entary schools is sim ilarly dominated by rote learning of nam es, definitions, and miscellaneous facts” (p. 82). Novak reported th a t many learners admitted learning by rote w ithout recognizing th a t another way of learning existed. Also, most students were not conscious 16

of the fact th a t learning is their responsibility. W andersee (1988) found th a t few er than h alf of th e c o llie students questioned claimed to use organizational tools when studying from a textbook and th a t only 6% of students questioned claimed to make a conscious effort to make connections between prior knowledge and new textbook concepts. These findings indicated th a t students are not approaching textbook study in m eaningful ways. Dickie (1994) examined the m eaningful learning orientation of college physics students in C anada and found th a t students “approached physics w ith the intention of memorizing form ulas rath er th an understanding concepts” (p. 33). In fact, only 5.6% of th e students had a deep approach or m eaningful approach to learning on th e pretest given a t the beginning of the course. This percentage illustrates the m agnitude of the problem of rote learning in college physics. Studies T hat Increased Some Aspect, of M eaningful Learning M oreira (1977) conducted a study in Brazil w ith students enrolled in a calculus-based second sem ester physics course and found th a t th ere w ere no differences on traditional achievement m easures between the experim ental group (Ausubelian organizational method) and the control group (traditional lecture method). This “finding suggests th a t the A usubelian approach was a t least as effective as the conventional approach, in term s of conventional achievem ent m easures” (M oriera, 1977, p. 62). Additional results revealed th a t th e degree of concept differentiation and the degree of association between related concepts were greater for the experim ental group based upon word association te sts and num erical association tests, respectively. Also, th e concept m aps of th e experim ental group were “qualitatively different fi-om those of th e control group students, and indicated b etter concept differentiation, more meaningful association and a hierarchical 17

disposition coherent w ith A usubel’s theory” (M oreira, 1977, p. 124). However, it seem s th a t th is outcome was ensured since he introduced th e experim ental group to concept m aps (concepts w ith linking words related to them) in the ‘notes’ sections and did not introduce them to th e control group. He concluded th a t teaching according to A usubelian theory produces greater concept learning, b u t not g reater achievement. Cullen (1983) examined concept learning in a college chem istry course to determ ine w hether or not a concept of m inor im portance could be raised to the position of a high order or subsum ing concept. He found th a t overt attem pts, via w ritten passages explaining the concept of entropy and describing how entropy explained phenomena observed in tiie laboratory, were effective for some students in improving th eir ability to show linkages between lower level concepts and a subsum ing concept In oth er words, some learners began to view the m inor concept as a subsum ing or higher level concept Only about one h alf of th e experim ental group responded to th e treatm ent and restructured th e ir conceptual structure. He concluded th a t there m ust be some "preexisting desire to acquire and use high-order concepts” (p. 109). Cullen (1983) claims his research findings "indicate th a t careful preparation of m eaningful instructional m aterials w ill not alone resu lt in all students grasping the significance of high order concepts” (p. 110). He claimed th a t educators can and m ust help students understand th e need for conceptual learning. Based on th is work, advance organizers sim ilar to Cullen’s treatm en t should cause some physics students to le am more meaningfiilly. Taylor (1985) examined th e thinking, feeling, and acting of 30 college biology students who were ta u g h t a laboratory in which concept m aps, Vee diagrams, and questioning techniques were implemented. Ta)dor claim ed the use of these tools combined w ith a leam ing-how-to-leam focus changed the 18

m eaning of the laboratory for h er stu dents. H er students rated th e laboratory course higher on end-of-sem ester evaluations th a n th e rem aining students in the course who had other laboratory activities. O n th e evaluation, her students also claim ed to have learned more biology and rated highly the use of concept maps and Vee diagram s in the laboratory. T a^ o r concluded th a t empowering the stu den ts so th a t th eir m eaning of a laboratoiy or course is changed requires educators to provide th e tools and experiences w ith which they can leam to leam meaningfully. M eaningful learning is necessary for students’ m eaning of an educational eiq)erience to be changed as well as for them to integrate thinking-feeling-acting. From tM s, it seem s possible th a t concept maps, Vee diagram s, and questioning in the physics lab could also cause the thinking-feeling-acting th a t is consistent w ith m eaningful learning. Bar-Lavie (1987) conducted research w ith 11th grade stu d en ts of environm ental science in Israel. H e tau g h t a version of N ovak and Gowin’s (1984) Learning How to Leam (LHTL) course before the stu d en ts took p a rt in an environm ental science field program . S tudent achievem ent improved 80% after the LHTL course and continued to improve throughout th e field program. The LHTL program improved both integrative thinking and hierarchical organization to a g reater degree th an was achieved in th e field program. M eaningful leam ers continued to improve their ability to integrate concepts in field settings; w hereas, rote leam ers failed to in teg rate concepts when in a field setting. He found th a t m eaningful learners had higher achievem ent scores th an rote leam ers and th a t objective evaluations did not detect as great a difference in the learn ers’ achievem ent as w as detected when evaluated by other methods such as concept mapping or interview s. Bar-Lavie (1987) also found th a t th e environm ental science field p rc ^ a m increased the rate o f‘‘thinking-feeling-acting” (p, 127) behavior. This 19

behavior is consistent with m eaningful learning. However, m eaningful leam ers tended to integrate th e “thinking-feeling-acting” behavior as m uch in school as in th e field while rote leam ers tended to integrate the behavior more in the field setting. These findings about concept m aps and m eaningful learning courses are easily applicable to the m eaningful verbal reception learning treatm en t this study proposed. Jegede, Alaiyemda, and Okebukola (1989) found th a t concept mapping instruction w as m ore effective (p < .01) th an trad itio n al expository instruction in enhancing m eaningful learning of a 10th grade biology course. The concept m apping group h ad greater achievem ent as well as less anxiety th an the expository group. Jegede, Alaiyemda, and Okebukola (1989) concluded th a t “concept m apping promotes m eaningful learning” (p. 7). Amir and Tam ir (1994) found th a t rem edial activity m aterials significsmtly (p < .01) improved the understanding of photosynthesis and respiration for 11th and 12th grade students. T he rem edial m aterials were designed to prom ote progressive differentiation of photosynthesis and respiration. Once the concepts were differentiated, th e num ber of misconceptions th e students h ad about these topics tended to decrease. This study found th a t m eaningful learning of concepts can be taught by th e appropriate use of rem edial m aterials. This supports th e use of advance organizers in a m eaningful verbal reception learning treatm ent. Studies R elating Meaningful Tjeaming O rientation. P rior Knowledge, or Meaningful U nderstanding to O ther Variables Ausubel claim ed prior knowledge affects cognitive structure and subsequent m eaningful learning. However, th ere w as little evidence to support his claim . Pines and N ovak (1985) indicated a need for em pirical tests of A usubelian theory because of the absence of support for his claims. The authors exam ined the effects of an A usubelian-based audio-tutorial 20

science treatm ent for first and second grade students to gain i n s i s t about prior knowledge and to determ ine w hether or not instruction was effective. Children’s propositions were examined since th e num ber of propositions a student exhibits is indicative of th e d ^ re e of differentiation and integration of the concept. Hence, if the num ber of propositions is greater after instruction, meaningful learning occurred. They found th a t audio-tutorial instruction was effective in creating valid concepts in children. Pines and Novak (1986) concluded th a t prior knowledge did affect post instruction concept knowledge. This conclusion provides support for Ausubelian theory in which new learning is related to prior knowledge. BouJaoude (1992) exam ined the relationships among h i ^ school students’ learning approaches, th eir prior knowledge and attitu des toward chem istry, and their chem istry m isunderstanding score. Also, th e differences between rote and m eaningful leam ers were examined. The sam ple consisted of high school students tau g h t by lecture and laboratory. Findings revealed th a t the pretest m isunderstandings and the students’ learning approach accounted for a statistically significant (p < .01) proportion of th e variance on the chem istry m isunderstandings test. They found th e m eaningful learners performed significantly (p < .0001) better th an the rote learners on th e m isunderstanding m easure (BouJaoude, 1992). The reason given for this finding was th at m eaningful learners appear better able to relate inform ation acquired in the classroom to th eir prior knowledge and store the inform ation in bigger, more organized chunks. W hen more of the inform ation about a subject is organized together, misconceptions are easier to correct. O n the other hand, rote leam ers store th eir inform ation in sm aller chunks. BouJaoude (1992) concluded it is necessary to teach students how to be meaningful leam ers. This study provides evidence th a t prior knowledge, as well as meaningful learning orientation should be variables included as 21

predictors of meaningfiil understanding or physics. Also, it supports th e need for students to possess a greater m eaningful learning orientation since these students had greater understanding. Ram sden and Entw istle (1981) exam ined th ree factors of approaches or orientations to studying: personal m eaning, reproducing, and achieving and found th a t meaningful learning orientation was positively related to achievem ent, while th e reproducing orientation had a negative relationship. S tudents indicated th a t the approach used depended upon the m anner in which th e te st was taught. Conclusions w ere th a t good teaching, freedom in learning, and not overloading are good practices th a t would promote deep learning orientations. These changes should also promote the qualify of w hat is learned. This study is applicable to the proposed study in th a t it provides evidence th a t m eaningful learning orientation is related to achievem ent and treatm en t. E ntw istle and W aterston (1988) exam ined students’ sfgdes of studying w ith revised versions of two inventories. One was derived from cognitive psychology and the other from research. The Approaches to Studying Inventory suggested four m ain orientations: achieving (career m otivation, hope for success), m eaning (deep approach and intrinsic m otivation), reproducing (surface approach and fear of failure) emd non-academic (social m otivation and negative attitudes) (Entw istle & W aterston, 1988). The Inventory of L earning Processes also suggested four m ain orientations: deep processing (evaluates and compares), elaborative processing (incorporates own terminology), fact retention, methodical study (study guide type activities). The two inventories had very close agreem ent betw een each set of scales. The authors rem inded us th a t "approaches to studying are a product of th e interaction between characteristics of individual stu d en ts and th eir perceptions of the courses, teaching, and assessm ent procedures” 22

(Entw istle & W aterston, 1988, p. 264). Hence, attem p ts to a lte r a stu d en t’s study strategies will be more effective if th e learning environm ent is also changed so th a t th e students will perceive th e rew ards o f improved methods of studying. They em phasized th a t "rote learning is negatively related to fact retention am ong scientists” (Entw istle & W aterston, 1988, p. 262). In other words, students who had a surface approach had less reten tio n of read factual m aterial th an those who had a deep approach. T his finding is supported theoretically hy the idea th a t facts are held m ore effectively when th ere are more m eaningful linkages th a n w hen they are stored w ith one linkage as is done in rote learning. Edmondson and Novak (1993) focused on research dealing w ith students’ epistem ological views and th eir learning strategies. Those w ith positivist views of science believe th a t science can he learn ed hy objective observation. Those w ith a constructivist approach believe th a t knowledge is constructed using previous knowledge as a base. The au th o rs em phatically endorsed th e adoption of a constructivist epistem ological order to advocate m eaningful learning. A high level of integration is not possible w hen two or more system s of knowledge do not intersect. T his paralleU zation invites rote learning as th e m ost efficient method of learning if knowledge is absolute. This research indicated th a t typical elem entary and college science courses tend to reinforce th e positivistic epistemological view w hich fu rth er fuels rote orientations. The authors suggest th a t teachers m ake epistem ological issues explicit and em phasize the active role of th e learn er in construction of knowledge ju s t as real scientists do. The hypothesis is th a t stu dents tend to gravitate tow ard a learning approach th a t is consistent w ith th eir epistemology. Therefore, in order to change th e ir learning orientation, one m u st ensure a constructivist epistemology. These recom m endations support both treatm en ts proposed in this study. 23

Dickie (1994) examined college physics students’ approaches to learning, th e intellectual dem and of assessm ent item s, an d th e relationships between stu den ts’ approaches to learning, th e intellectual dem ands of assessm ent, and th e students’ performance in th e course. H e found th a t students “approached physics w ith the intention of m em orizing form ulas rath e r th a n understanding concepts” (Dickie, 1994, p. 33). O nly 5.6% of the students had a deep approach to learning on th e p retest, w hile m ost had a surface or achieving approach (Dickie, 1994). However, after two sem esters of physics instruction, the percentages of th e students having surface approaches and deep approaches increased w hile the percentages of those having achieving approaches decreased. S till, only 20% o f students reported they tried to understand physics concepts (Dickie, 1994). F urtherm ore, ttests com paring th e pretest and p osttest approach to learn in g m eans revealed a significant

(p < .08) increase in surface approaches, no

significant differences in the deep approach, and a significant (p < .03) decrease in the achieving approach. Hence, two sem esters of physics had increased students’ surface approaches and decreased th e ir achieving approaches. U sing a modified version of Bloom’s taxonomy, D ickie categorized the intellectual dem ands of assessm ent item s. (Correlations betw een students’ physics understanding as m easured by course assessm ent item s and the achieving approach were positively correlated, w hile th e deep approach was negatively correlated w ith physics understanding. He e3q)lained th a t only 6.6% of th e assessm ent item s for th a t course w ere categorized a t the com prehensive level. Students were not rew arded on assessm ent item s for possessing a deep approach; hence, they abandoned it. F or th e second sem ester, over one th ird of the item s were a t th e com prehension level. This finding agreed w ith the shift of students’ approach aw ay from a surface 24

approach in the second sem ester. Although statistical analyses were not calculated, he found th at, in general, students w ith a deep or deep achieving approach were more successful th a n students w ith a surface approach (Dickie, 1994). Dickie (1994) also exam ined the relationship of grade in the course and approach to learning. The only significant correlation betw een approach to learning and grade on the final exam ination was a negative correlation betw een achievem ent on th e final exam ination in the second course and having a surface approach. P erh ap s a m ore significant finding was the relationship between students’ approach to learning and th e ir scores on the Force Concept Inventory (FCD. S tudents w ith a deep approach scored significantly higher on the FC I th a n those w ith a surface (p < .012) or achieving approach (p < .001) an d higher also than those w ith a deep achieving approach (p < .005) o r a surface achieving approach (p < .003). T hus, the approach to learning m easure was able to select those students who had an accurate conceptual understanding of Newton’s laws of force since the FCI required "conceptual understanding rather th a n rote application of Newton’s laws” (Dickie, 1994, p. 55). Based upon these findings, he suggests educators adopt strategies and assessm ent item s th a t encourage meaningful learning, for m eaningful learning m eans improved understanding. H e also used a variefy of m easures on different levels of Bloom’s taxonomy scale to m easure m eaningful learning. This study provides the basis for my use of high-level questions and problem-solving to m easure m eaningful understanding. The study also supports the use of m eaningful learning orientation as a variable to predict m eaningful understanding of physics concepts. To add fu rth er credibility to the aim s of th is proposal, Dickie em phasizes th e fact th a t meaningfully-oriented students are more successful in physics th a n rotely-oriented students. 25

Consequently, a treatm en t th a t would cause students to approach learnin g in a more m eaningful way would be of g re a t value. Cavallo and Schafer (1994) found th a t students’ prior knowledge of meiosis and th e ir m eaningful learning orientation were significant predictors of high school biology students’ m eaningfiil understanding of th e P unnettsquare method and m eiosis as well as th e relationships between th e two topics. Prediction strength was independent of th a t explained by ap titu de and achievem ent motivation. The interaction of meaningful learning and prior knowledge significantly predicted m eiosis understanding, process and conceptual relationship understanding, and understanding m easured by relationship statem ents about meiosis and th e Punnett-square m ethod. They found no significant differences, except for those students who w ere m idrange on th e m eaningful learning continuum , on meaningful understanding betw een generative and receptive treatm ents. The findings of this study support the inclusion of prior knowledge and meaningful learning orientation to predict meaningful understanding. Cavallo (1996) m easured high school biology students’ m eaningful learning orientation, reasoning ability, genetics meaning, genetics problem solving, and m ental model knowledge of genetics. She determ ined th a t th ere WEIS no significant relationship between high school students’ m eaningful learning orientation fuid reasoning ability (r = .08, p < .05). F urtherm ore, students’ reasoning ability was not significantiy correlated w ith th e ir m ental model scores, a m easure of meaningful understanding. Cavfdlo (1995) examined th e vEuiables th a t best predicted perform ance on th ree te sts (test of genetics mcEuiing, te st of genetics problem solving, suid m ental models). She described m ental modeling Eis "eui open ended assessm ent m ethod th a t revefds the extent smd nature (conceptual knowledge or procedurfd knowledge) of students’ imderstcmding of a given topic” (p. 12). She also found 26

th at students’ m eaningful learning orientation and reasoning abiUly predicted scores on genetics m eaning, b u t meaningful learnin g orientation was the better predictor. T he stu d en ts’ reasoning abiUty an d m eaningful learning orientation predicted stu d en ts’ achievem ent on te sts of genetics problem solving, b u t reasoning ability was the b etter predictor. Cavallo (1996) compared the stu d en ts’ m ental models w ith th e m ental models of students in a previous study and found th a t the two groups of stu d en ts had very sim ilar m ental model frequencies. She introduced th e use of m ental models and problem solving to m easure m eaningful understanding of genetics. F u rth er study should be conducted th a t investigates th e use of sim ilar m easures in physics. Lawson and Thom pson (1988), R enner, A braham , Grzybowski, and M arek (1990), and W illiam s and Cavallo (1995) found th a t students w ith higher reasoning ability had greater understandings or fewer misconceptions. The findings by W illiam s and Cavallo (1995) about reasoning ability and meaningful learning orientation contradict those of Cavallo (1996). F u rth er research should be conducted w ith different m eaningful understanding m easures to determ ine if reasoning ability and not m eaningful learning orientation are b etter predictors of m eaningful understanding of physics concepts. W estbrook an d M arek (1991) found th a t none of th e ir 7th-graders, lO th-graders, or u n iv ersity students of biology possessed a complete understanding of th e difhision concept. Concept evaluation statem ents were evaluated to determ ine th e students’ understanding of th e concept of diffusion. They found th e students were not appreciably different in the degree of understanding of diffusion despite th e d isp arity in age. In fact, 55% of the 7th-graders h ad misconceptions about diffusion, w hereas 65% of th e lO th-graders and 61% of th e college students h ad m isconceptions about 27

diffusion. It seems th a t g reater exposure to diffusion only gave th e more advanced students m ore term s to m isuse rath e r th a n increasing th eir understanding. A sim ilar stu dy by W estbrook and M arek (1992) exam ined th e three age groups of students’ understanding of the concept of hom eostasis. The results were very m uch th e same: There was very little understanding of the concept of hom eostasis across th e th ree age levels exam ined. O nly 3% of the 7th-graders had p artial understanding while the rest of them had no understanding or did n o t respond to th e question. None of th e lOth-graders had complete understanding and only 12% had p artial understanding. Roughly, one-third of th e college students had a complete or p artial understanding of hom eostasis. A g reat m any of each age-level exhibited misconceptions (46%, 54%, and 64% respectively). A lack o f understanding was pervasive across th e grade levels. There was a trend tow ard greater understanding for those w ith greater cognitive reasoning. In spite of having studied the concept of hom eostasis m ultiple tim es, students still could not grasp the form al concept. Studies on Concent M ans or Vee Diagram s (Concept m aps w ere defined as concepts (perceived relationships w ithin a group of objects or events) and linking words (H einze-Fry & Novak, 1990). Novak (1984) provided exam ples of concept maps and described their use. Ooncept m aps m u st contain concepts, propositions, hierarchy, examples, and cross links. The hierarchical organization o f a concept map requires the student to determ ine th e m ost inclusive concept for a topic (superordinate). S tu dents’ concept m aps are evaluated by assessing the propositions, hierarchy, and cross links. Propositions indicate the relationships among concepts which is indicative of th e degree of differentiation of concepts. The num ber of hierarchies indicate th e extent of 28

the differentiation. Examples are critical in m eaningful learning since they aid stu d en ts in anchoring new knowledge to prior knowledge. The num ber of cross links indicate the degree of integrative reconciliation. According to this model, m eaningful understanding can be promoted and assessed using concept m aps. N ovak (1984) complained th a t students in typical science laboratories rarely attend to th e phenomena being observed and rarely question them selves as to w hat concepts, principles, or theories w ere im portant in understanding th e laboratory concepts. Hence, laboratory work and lectures becam e separate knowledge entities. Novak suggests th a t educators in stru c t students not only in th e key elem ents of the Vee, h u t also in its use as a tool to in terp ret laboratory work. Vee diagram s w ere defined as heuristic devices th a t represent th e interplay between concepts, principles, and theories w ith observations and recorded data. The Vee consists of th e key elem ents of. theory, principles, concepts, events, records or data, transform ation of data, and knowledge claim s. Novak claim s th e Vee allows stu dents to conceptualize th e ir laboratory work. Novak, Gowin, and Johansen (1983) found th a t seventh and eighth grade stu d en ts could successfully construct concept m aps, b u t th a t m any lacked cross-linkages. Perhaps instruction on concept m aps did not properly em phasize the im portance of cross links. On the other hand, the lack of cross-linkages m ay indicate the students’ failure to utilize integrative reconciliation because this age level m ay leam m aterial in discrete bits. S tudents who used th e Vee and concept m aps scored significantly higher th an th e non-m apping students on solving novel problems. Since th e correlation between achievem ent and m apping perform ance w as low, m apping m ust m easure a different ability th a n th e typical achievem ent tests do. M apping could broaden the teacher’s arsenal of evaluation tools. 29

N ovak (1993) described a previous study (Bacones & Novak, 1985) in which stu d en ts who did concept m aps had significantly (F=480) few er m isconceptions th an students who did regular problem sets. Evidence suggests th a t concept maps assist stu d en ts in th e m eaningful learning needed for the elim ination of misconceptions and subsequent m eaningful understanding. H einze-Fry and Novak (1990) exam ined th e concept m apping and stu d en t attitu des in an auto tu to rial college biology course. S tudents w ith higher SAT scores tended to benefit th e m ost fix)m mapping, althougdi It w as hypothesized th a t the lower SAT stu dents m ight benefit fi*om longer term m apping treatm ent. Analyses revealed th a t m apping tended to increase stu den ts’ clarity, integration, and retention. Comments or attitu d es about m apping content were generally positive, although some expressed fru stratio n w hen new concepts did n ot fit into th eir old existing structures. Trowbridge and W andersee (1994) exam ined questionnaires, instructor interview s, and the concept m aps of students enrolled in a college course on evolution to determ ine if evidence for critical junctures m ight be found. Also, the research sought to determ ine if concept m apping is viable in a college course on evolution. They defined critical junctures as "a conceptual w atershed th a t divides students into two groups on the basis of th e ir prior understanding of fundam ental concepts relevant to those currently being taugh t” (Trowbridge & W andersee, 1994, p. 461). In other words, a critical ju n ctu re is th e point in a science course a t w hich students m ust possess essential understanding of previous concepts before new concepts m ay be understood. C ritical junctures were found by noting the confusion and un certainty students had in identifying superordinate concepts. One th ird of the in stru cto r comments to students about concept maps were regarding th e lack of linking words. Seventeen percent of the instructor comments w ere 30

statem ents calling for m ore examples. Instructors m ay use concept maps to determ ine w hether or not m eaningful learning has occurred by the evaluation of concept m aps after critical junctures. Poorly constructed maps indicate little m eaningful learning has occurred. O ther findings revealed students spent considerable tim e constructing m aps and th u s, spent more tim e attem pting m eaningful learning. They also adm itted spending 37% more tim e studying for th e course (Trowbridge and W andersee, 1994). These studies on concept mapping and Vee diagram s suggest that: (1) low ability stu d en ts can construct concept m aps an d Vee diagram s; (2) concept m aps and Vee diagram s m easure som ething different th a n traditional achievem ent te sts m easure; (3) those who m ake concept m aps have fewer m isconceptions; and (4) concept m ap use increases clarity, integration, retention, study tim e, and understanding. Studies about O ther Toola/Meana th a t Increase M eaningful L earning O rientation. M eaningfu l U nderstanding, or Meaninyfiil T^jim ing O ther tools such as: audio-tutorial lessons, advance organizers, and questions have been studied w ith regard to th eir ability to increase some aspect of m eaningful learning. The following describe characteristics of m eaningful learning activities th a t have been found to increase m eaningful learning. Novak and M usonda (1991) developed audio-tutorial lessons (AT) for first and second grade stu den ts th a t would build upon one another so p ast lessons would serve as advance organizers for new m aterial. One group of children participated in th e AT lessons in first and second grade, while another group received no instruction. The children in th is study were interview ed to assess changes in science concepts. C oncept m aps were made from the interview s. Novak and M usonda (1991) found a significant (p < .015) increase in th e valid notions of students fh>m grades two through 31

twelve. The AT in structed students had higher concept m ap scores a t every grade level. Thus, th e 60 AT lessons served as advance organizers for the students when they enrolled in science courses later. Advance organizers assist students in resolving conflicting conceptions w hich promotes meaningful learning. T his only occurs when knowledge becomes intertwined, hence, to resolve m isconceptions is to leam meaningfully. Purdom and K rom rey (1992) examined the effects of instructor intervention in cooperative learning on the achievem ent of elem entary education mtyors in coll^;e who w ere enrolled in a curriculum course. One group had no instructor assistance; in another group, advance oiganizers were given by the in stru cto r before cooperative learning; and in another group, the instructor conducted question and answ er sessions after cooperative learning. T hey concluded th a t advance organizers improve learning more th an post-session discussions or cooperative learning alone. Ruhin and T a m ir (1 9 8 8 ) found th a t fa m iliar advance organizers combined w ith application-lahoratory tasks improve students’ understanding of the rules of scientific inquiry. Students having the advance organizers significantly (p < .001) outperform ed the control students on tests of process skills in which they w ere required to analyze research and identify the hypothesis, th e variables controlled, and conclusions. They also outperformed th e control group on practical tests of problem solving and the advance organizers helped th e w eaker students most. S tudents’ attitudes toward investigative laboratories were more positive th a n those attitudes toward verification laboratories. Glover, Bullock, and D ietzer (1990) examined th e type of delay between advance organizer use and the subsequent reading of tex t to understand conditions th a t optim ize advance organizer use. They found th a t when as much as 10 m inutes of inactivity or activity in another subject was 32

placed between the reading and paraphrasing of the advance organizer, the subjects recalled significantiy (p < .01) more of th e text th an w hen th e advance organizer was im m ediately followed hy th e reading of th e tex t w ithout the delay. It was hypothesized th a t the delay provided sufficient tim e for th e exact form of the advance organizer text and previous knowledge lin k s to be forgotten. This causes extra processing which should enhance

m eaningful learning since prior knowledge is re-anchored to new ideas or concepts. Arm hruster, Anderson, A rm strong, Wise, Janisch, and M eyer (1991) claim th a t factual, memory-type of questions "are not likely to prom ote conceptual understanding and m eaningful learning” (p. 37). Teachers should ask higher-order cognitive level questions to have students apply learning. Too ofien teachers ask low-level cognitive-level questions to check recall of knowledge. Other authors, Menke and Pressley (1994), had sim ilar findings: M eaningful learning can he promoted hy questioning activity which leads the students to tie new inform ation to prior knowledge. This questioning, called elaborative interrogation (El), requires students to generate elaborations which facilitates learning even if th e ir responses to the questions are poor. Q uestions force leam ers to connect prior knowledge w ith new facts. P iagetian Theory Piaget believed th a t leam ers construct knowledge. However, Piaget differs from Ausuhel on how th a t knowledge is constructed. According to Piaget, when a leam er encounters in p u t from the environment, th e leam er’s schemes or m ental structures incorporate th e experiences or d ata. H e called this cognitive process assim ilation. A ssim ilation is a quantitative and qualitative change in existing schem es or m ental structures. A schem e is "w hatever is repeatable and/or generalizahle in an action” (Renner & M arek, 1988, p. 30). In other words, schemes are "m ental d ata processing 33

procedures” (R enner & M arek, 1988, p. 30). The schem e is th e basic u n it of cognitive structure; w hereas, the integration of schemes form w hat are called cognitive or m ental structures. If and w hen newly assim ilated inform ation conflicts w ith previously formed m ental structures, the resu lt is called disequilibrium (M arek & Cavallo, 1997). Disequilibrium serves to m otivate the leam er to seek equilibrium . W ithout disequilibrium , schem ata would not qualitatively change. Regaining equilibrium or cognitive harm ony resu lts in w hat Piaget called accommodation. Accommodation is in the developm ent of new m ental structures. This "accord of thought w ith things” w as w hat Piaget called adaptation (Piaget, 1963, p. 8). Thus, assim ilation and accommodation represent th e learner’s adaptation to th e environm ental input. For Piaget, learning is still incomplete. The leam er m ust then organize the new or newly modified m ental stru ctu re w ith previously existing m ental structures. P iaget called th is process organization, or in his words: "the accord of thought w ith itself* (Piaget, 1963, p. 8). In organization, structure placem ent or the interconnectedness are examined and modified so they are in accord w ith one another. The processes of assim ilation, accommodation, and organization are called functional invariants of intelligence. By functionally invariant, P iaget m eant th a t all leam ers go through th e sam e order of processes regardless of age. P iaget em phasized th a t the types of m ental stru ctu res and content (i.e. concrete or hypothetico-deductive) vary w ith the leam er’s age. Piaget described four cognitive stages of development: sensori motor, preoperational, concrete operational, and formal operational (R enner & M arek, 1988). h i th e sensori m otor stage (from about 0-2 yrs.) th e child uses sensory experience to construct schem es and leam to attach sounds to experiences, th u s language develops. D uring th is stage children develop 34

object perm anence from th eir experiences. There is no internal representation of objects or events in this stage. In th e preoperational stage (about 2-7 or 8 years of age) th e child is capable of seeing and reporting. Thus, th e child has acquired th e ability to internally represen t objects and events. However, th e child is egocentric (cannot tak e others* view points), cannot reverse thinking, centers on aspects of perception, cannot see stages in a transform ation, uses transductive reasoning, and cannot conserve various quantities. In th e concrete operational stage (about 7-11+ yrs.), the leam er can do all of th e m ental operations listed above th a t he or she w as not capable of as a preoperational leam er. According to Piaget, the concrete operational le am e r is bound to the world of experience and concrete objects. Thought is logical, b u t not y et optim ally so in th a t the leam er can n o t consider all possibilities and hypothetical situations. The formal operational stage (begins around 11-15+ yrs of age) em braces hypothetical-deductive reasoning, scientifrc-inductive reasoning, and reflective abstraction (W adsworth, 1989). Form al operational thought is the pinnacle o f reasoning. Piaget believed th a t such reasoning was independent of all subject m atter and th a t form al reasoning followed the rules of propositional logic (Inhelder & Piaget, 1958). Form al reasoning is determ ined by the acquisition o f five abilities: proportional logic, probabilistic reasoning, the separation of variables, com binatorial logic, and correlational reasoning (Tobin & Capie, 1981). Piaget (1970) stressed th a t the development of the intellect is dependent upon n atu ral processes and th a t it m ay be accelerated by education, b u t th a t it is not derived from th a t education. Piaget stated th a t experience, social interaction, equilibration, and m aturation are th e factors th a t affect cognitive developm ent (M arek & Cavallo, 1997). L earning occurs b est in an environm ent w hich allows and stresses self regulation, ejq)erience, and social 35

interaction. Piaget suggests educators provide children with activities in which they m ay explore concepts a t th eir stage of development. This acts to build the strongest foundation for th e succeeding stages rath er th an acting blindly to accelerate stage developm ent (Labinowicz, 1980). Research in P iagetian Theorv-Piagetian Stage Studies M any researchers have found th a t the transitio n to formal operations or reflective thinking is not occurring, or has not developed by the tim e m any students enter college. Resnick and Ford (1981) cited th a t the people in a few cultures never become reflective or formal operational thinkers. McKinnon and R enner (1971) found th a t 50% of th e college freshm en tested w ere concrete operational or intuitive and th a t another 25% were not fully formal. Schwebel (1975) found th a t 17% of th e college freshm en tested were concrete operational; 63% w ere a t th e lower formal level; w hile only 20% were a t the upper formal level. T he results of a seven-college study (Renner, e t al., 1976) are no more encouraging. The percentage of fully reflective college students ranges from 12% to 61% among the seven institutions studied. C hiappetta (1976) compiled a table of studies of secondary and college age students. He concluded th a t m ost have not yet reached the reflective or formal operational stage. Billeh and K halili (1982) investigated cognitive development and the relationship betw een cognitive development and physics comprehension of llth -g rad e Jordanian students. They found th a t only 17% of th eir sample was formal operational. They found th a t cognitive level is a significant factor in the com prehension of concrete concepts on the achievem ent test. T hat is, the higher th e cognitive level, th e better the comprehension of concrete concepts. They found formal operational ability aids in the understanding of formal as well as concrete concepts. R enner (1986) reported th a t it appears the num bers of concrete 36

operational thinkers leaving our schools is increasing. More recently, Trifone (1991) found th a t after using the Test of Logical Thinking (TOLT) in the assessm ent of developmental level th a t more th a n 76% of high school freshm en and about 60% of high school sophomores were still intuitive. Based upon finding high percentages of intuitive or concrete thinkers in high school, Trifone cautioned against teaching formed concepts to concrete thinkers because of em increased risk of creating misconceptions. Simply being concrete operational m eans th a t th e possession of hyptheticodeductive reasoning is absent emd w ithout it th e student ceumot compare competing hypotheses. These studies span m any decades and indicate th a t m any American students are not able to m ake use of the form al thought structures. This is of concern in this study since W illiams and Cavallo (1995) found reasoning ability to be a better predictor of m eaningful understanding of physics concepts. Reasoning ability m ust be exam ined in order to assess its relationship to meaningful learning orientation and m eaningful understanding in physics. Lawson's Modified Version of P iagetian Stage Theory Piaget’s stage model is perhaps the m ost arguable p a rt of his theory. “A long line of research indicates clearly th a t, although advances in reasoning performance do occur during adolescence, no one, including professional logisticians, reasons w ith logical rules divorced fi*om the subject m atter" (Lawson, 1995, p. 102). Therefore, Lawson suggests a modified version of Piagetian stage theory. Lawson (1995) chooses to view th e p attern s of *1f... and... then” (p. 107) thinking across each age. In w hat Piaget called the sensori-motor stage, children’s behavior follows th e if... and ...then behavior. The child has the ability to em pirically rep resen t w hat was experienced. Thus, Lawson called th is stage: stage one of preverbal deductive thinking. Lawson called w hat P iaget called the preoperational stage th e second stage 37

of preverbal deductive thinking. The child still th ink s w ith th e if . and. .then pattern, b u t th e child has th e ability to in itiate hypothetical m ental representations. In other words, the child can represen t som ething th a t has not been experienced. Piagetfs concrete operational stage is Lawson’s stage three of verbal deductive thinking. In th is stage, Lawson claims th e child verbally applies th e if...and...then p attern to em pirical propositions. Representations initiate th eir em pirical thinking w hich is inductive in nature. He calls those in stage th ree intuitive thinkers. The P iagetian formal operational stage parallels Lawson’s stage four called verbal deductive thinking. Once more, the if...and...then p attern is applied as it has been throughout development. Only hypothetical representations initiate thinking which is abductive in nature. The stage four child is "deflective, selfcontained, and proactive” (Lawson, 1996, p. 112). J u s t as Piaget claim ed, stage three children’s thinking begins w ith the real, w hile stage four adolescents’ thinking begins w ith th e possible. Lawson (1995) states, “although P iag ef s characterization of adolescent thought in term s of form al operations appears to be incorrect, his characterization of adolescent thought in term s of its hypothetical, as opposed to em pirical, n atu re appears right on targ et” (p. 103). R esearchers (R enner & M arek, 1988) have found th a t concrete operational learners do not leam formal concepts. Likewise, preoperational learners do not leam concrete concepts. In theory, it is th e student’s attem pt to leam concepts th a t are above his or her reasoning ability th a t results in misconceptions. Concrete leam ers are capable of reasoning w ith th e concrete aspects of a concept, so w hen they attem pt to reason w ith the formal aspect of a concept they often form m isconceptions (Renner & M arek, 1988). The m ental stru ctu res of th e various stages are indeed, qualitatively different. Yet, th e stru ctures eventually become q uantitatively more 38

complex u n til th e learner advances to the next stage. Changes occur in the way th a t th e learner can apply a particular th ink ing pattern. A novel w ay of applying a particular thinking p attern brings w ith it more sophisticated reasoning which, over tim e, readies th e learner’s ability to apply yet another novel thin kin g pattern. This process of developm ent is continuous, yet distinct reasoning p attern s occur w ithin the continuum of overall development. The Learning Cycle The learning cycle consists of th ree phases: e^xloration, conceptual invention (or term introduction), and application (form erly e3q)ansion) (M arek & Cavallo, 1997). D uring exploration students in te ra ct w ith m aterials under teacher guidance, b u t y et in a structured way designed to promote assim ilation and disequilibrium . P iaget believed th a t leam ers m ust experience in order to get th e inform ation or essence of som ething into th eir cognitive structures. The exploration provides th e opportuniiy for eiq)erience and social interaction as students gather data associated w ith the concept to be assim ilated. In th e conceptual invention phase of th e learning cycle, th e teacher uses th e d ata from all students in a class and, by asking probing questions of the stud ents, leads them to recognize the p attern or regularity in the data. Once th e students construct th e regularity or p attern (concept), th e teacher attaches th e proper term inology if the students do not know the terminology. The conceptual invention phase of the learning cycle provides for the accommodation of P iaget’s model of intelligence. The conceptual invention provides an opportunity frr experience in m anipulating d ata and interacting w ith others as students discuss d ata and construct the concept. It also provides an opportunity for equilibration. J u s t as Piagetian theory did not end w ith th e process of 39

accommodation, the learning cycle does not end w ith conceptual invention. The th ird phase of the learning cycle, the expansion or concept application, requires th e students to use the newly learned concept and th e new term inology in different situations or w ith different m aterials. The e3q)ansion allows stu den ts the opportunity to organize th eir th o u ^ ts . This phase provides for the organization process of the Piagetian model. Therefore, the learning cycle explicitly provides the opportunity and activities for assim ilation, accommodation, and organization through providing experiences, social interaction, and tim e for equilibration. W hy should the learning cycle be used to teach science? R enner and M arek (1990) proport th a t th e learning cycle is an effective science teaching procedure since it is based on a sound theory base which “m u st include educational purpose, th e discipline of science, and a model for learning^ (p. 241). According to the Educational Policies (Commission (1961), schools’ purpose should be to teach students to think. The learning cycle m eets th is requirem ent since it relies upon building students’rational powers: recalling, im agining, classifying, generalizing, comparing, evaluating, analyzing, synthesizing, deducing, and inferring. W ith respect to being consistent w ith the discipline of science, students (during a learning cycle) perform activities th a t let them quest for knowledge which |g science. W ith regard to th e model of learning, th e learning cycle was derived from the Piagetian model. In other words, th e learning cycle is based upon a sound educational theory base. The L earning Cvcle and Sim ilarities of Piagetian Theory to A usubelian IhsQEX T he Piagetian theory of learning as incorporated in th e learning cycle is very sim ilar to Ausubel’s theory of m eaningful learning. In organization the “new stru ctu re is placed among all of the other structu res” (Renner & M arek, 1988, p. 32). Recall, also, th a t the expansion or concept application phase of 40

the learning cycle provides for organization by allowing th e learner to relate the new concept to o th er known concepts or to examine different aspects of the newly learned concept. The learner m ust detect sim ilarities, differences and other relationships betw een the new and old structures. This process of organization seems very close to Ausubel’s meaningful learning. Ausubel defined m eaningful learning as relating the elem ents of a ta sk "in a nonarbitrary, substantive fashion to w hat the learner already knows” (Ausubel, 1963, p. 18). The m eaningful learning and organization definitions appear virtually the same. P erhaps meaningful learning is w hat occurs during th e conceptual application (expansion) phase of a learning cycle? Providing tim e and activities in eipansion to allow students to m eaningfully leam , m ay give more students the opportunity to organize w hat they know. Theoretically the learning cycle is designed to cause students’ m eaningful learning. The following research about aspects of the learning cycle describe various advantages of using th e learning cycle (improved reasoning ability, achievement, and concept understanding). Learning Cycle Research Research on th e learning cycle will be sum m arized and categorized into four areas: studies show ing the effects of th e learning cycle on (1) reasoning ability, (2) achievem ent, (3) concept understanding, and (4) m eaningful understanding. T im in g Cvcle Studies and Reasoning Ability Renner, et al. (1976) provided two different studies of curriculum th a t claimed to move the learn er from the concrete level to th e formal operational level. The first dealt w ith eighth and ninth-grade junior high school courses. Three courses: Introductory Physical Science (IPS); Time, Space, and M atter (TSM), and Investigating the E arth-The E arth Science Curriculum Project (ESCP) all shared in th e prim ary goal of the development of problem­ 41

solving skills while encouraging experim entation and interaction with objects. The IPS (8th and 9th grade) curriculum provided investigations th a t attem pted to develop an understanding of th e stru ctu re of m atter. The TSM (8th grade) course presented problems which could he solved through observations and investigations. The ESCP (8th an d 9 th grade) course was more content oriented w itii designed investigations to m atch th e m aterial presented. A com parison study was m ade of these curriculum courses versus the traditional textbook curriculum . The num ber of form al leam ers increased from 6% to 40%. The TSM and th e IPS courses w ere found to account for the laig est gain in formal thinkers. The ESCP course was composed of m any form al concepts th a t w ere above th e developm ental level of the some students’ w hich m ight explain its lower success rate . This study shows th a t the TSM and IPS courses can he used to accelerate the concrete leam ers into formal thought. Perhaps sim ilar learning cycle treatm en t can accelerate college physics students’ reasoning ability. M arek and R enner (1979) examined an inquiry-based 10th grade biology class as com pared to a non-inquiiy class. T hey found th a t the students in the inquiry class had a greater increase in intellectual development, content achievem ent, inquiry skills (i.e. form ing hypotheses, designing e^)erim ents, interpreting data), and IQ scores th a n did the control students. They caution th a t for concrete leam ers, courses should utilize concrete experiences, concrete content, and concrete teaching procedures. M arek (1981) found th a t content achievem ent w as positively correlated w ith cognitive development, IQ, and inquiiy skills achievem ent (p > .05). Form al operational students had greater knowledge th a n the concrete operational students. Lawson and S nitgen (1982) cited sources th a t support th e prem ise th a t m any c o llie students fail to use form al reasoning. This study 42

attem pted to determ ine w hether or not a one-sem ester inquiiy-based biology course affects the developm ental level of the students, th e ir general intelligence, and th e ir degree of field independence. They found a significant difference in the p rete st and posttest m eans (p < 0.001) on th e Classroom Test of Form al Reasoning for th e pretested group. This supported th e prem ise th a t inquiry instruction promotes formal reasoning development. The overall posttest m ean score for the no pretest group w as slightly low er than the overall group m ean (p < .10). Therefore, sim ply taking the p rete st did slightly improve p o sttest performance. They suggest th e p retest acted somewhat like an advance organizer for reasoning. A nalysis of p retest and posttest gains for th e item s not taught showed no significant differences; thus nonspecific tran sfer did not occur. Lawson (1992) presented a brief sum m ary of the findings from biology education research. H e concluded th a t investigative, laboratory-based m aterials help college biology students acquire reasoning and process skills. Also, gains in reasoning w ere accompanied by equal or b etter achievem ent. He added th a t these gains appear to be general and long lasting. Such evidence supports th e prem ise th a t learning cycle instruction improves meaningful understanding once reasoning ability is improved. W estbrook and Rogers (1991) hypothesized “if th e students did not have to involve them selves in hypothesis testing, th e separation of variables, or other processes related to scientific investigation, then it seem s unlikely th a t the students would show gains on tests th a t m easure th e abUity to use those processes” (p. 7). In th e ir studies, three types of learning cycles about simple m achines w ere used. The three types of learning çycles present varying degrees of cognitive difficulty to the student. The control group conducted the descriptive learning cycle. Students observe phenom ena and describe it; they do n o t answ er “why” questions or design experim ents. 43

Another group used em pirical-abductive learning cycles, w hich present the students w ith *Vhy” questions. Students do not perform experim ents to answ er the questions, b u t rely upon the data already collected in order to answ er the questions. The la st group used hypothetico-deductive learning cycles. In these learning cycles a question is posed to which students design and perform experim ents th a t te st any hypotheses they set forth. Findings revealed th a t there were no significant differences am ong th e three treatm ents on reasoning ability. However, th e hypothetico-deductive group significantly outscored th e other groups on th e science process skills m easure as well as on one of the task s m easuring conditional/biconditional logic. Based on these results, W estbrook and Rogers (1991) concluded th a t providing th e opportunity for students to design experim ents, generate, and te st hypotheses enhanced th e use of conditional logic as well as science process skills. In addition, th e empirical-abductive and hypothetico-deductive learning cycles are more indicative of the tru e n atu re of science th an the descriptive learning cycles. They concluded th a t em pirical-abductive and hypothetico-deductive learning cycles are more advantageous to student learning because such learning cycles represent "real science” and they improve students’ science process skills and one aspect of th eir logical thinking. These results suggest the types of learning cycles th a t should be used in the proposed study. Adey and Shayer (1990), through the im plem entation of a two year research project, attem pted to accelerate th e developm ental level of B ritish adolescents. The interventions in physics, chem istry, and biology were designed to be related to ten formal operational schem ata. However, no attem pt was made to teach th e schem ata. Two of th e schools were middle schools (ages 11+ years). In each school control classes close in age and ability to the experim ental classes were chosen. P iagetian reasoning tasks 44

were used to obtain assessm ent of the developm ental level. They were adm inistered as pretests, m idtests (after one year of intervention activities), posttests (after two years), and delayed posttests (one year after posttests in laboratory school only). Adey and Shayer (1990) found th a t th e laboratory students’ reasoning scores were significantly higher than the control group a t th e posttestpretest com parison (p < .01), but also a t the delayed-pretest com parison (p < .05). So the experim ental group continued tow ard faster developmental advancem ent w ithout further treatm ent. The e3q>erimental group's cognitive developm ent w as statistically greater th a n th e control group's by .21 of a developm ental level or by .20 of a standard deviation. Regarding the case for general tran sfer of reasoning abilify, one of the schools was not allowed to use interventions concerned w ith the probability schem a. This school used interventions th a t dealt with other schema, then Piageffs pendulum ta sk and probability ta sk were adm inistered to these students and th e students from the control group. The intervention group having no probability interventions had p retest to posttest gains of 1.07 developm ental levels on the P iagetian Pendulum T ask and gains of 1.01 developmental levels on th e probability ta sk (Adey and Shayer, 1990). Gains on both tasks w ere significantly greater th a n the gains of the control group a t p < .01. Thus, evidence is given for general tran sfer success since th e probability schem a was not taught. They concluded th a t success on th e probability schem a m ust have come fi*om changes in cognitive ability due to th e other interventions. In a related study, (Shayer & Adey, 1992) exam ined th e ability of the P iagetian tests to predict science achievem ent scores and found th a t increased cognitive developmmit is not necessarily a condition for higher than norm al science achievem ent Residualized gain scores (rgs) are the difference of the grade achieved and the grade predicted. Large and positive rgs are 45

indicative of a successful intervention. The correlation betw een th e Piagetian posttests residualized g ain scores (rgs) and th e achievem ent science rgs was .34. They found th a t th e boys obtained 40% m ore grades o f C or higher in science th an th e control group. A bout 40% of th e boys an d 25% of th e girls science effect sizes w ere tw o stan d ard deviations above th e control group, b u t the other 60% of th e boys and 75% of the girls’ scores did n o t differ from the control group. The interventions appeared not to be dom ain-specific improvements as both boys and girls showed significantly higher achievem ent in E nglish on th e science achievem ent te st over th e control group. The effect size for th e boys scores was .32 of a stan d ard deviation, w hereas the effect size for th e girls w as .44 of a standard deviation. M ales in the experim ental group also showed a n im provem ent over th e control group in m ath w ith an effect size of .60 of a standard deviation. F inding increases in science, m ath, and E nglish achievem ent after science interventions support th eir hypothesis th a t th ese increases were caused by increases in developmental level. Such interventions m ust begin a t the developm ental level of th e learner and allow ei^lo ratio n , activity, and active developm ent of concepts for cognitive growth to occur. Some cases of success have been reported here, although in varying degrees. The degree of success depended upon the degree to which "optimal conflict" w as achieved. T rain a subject quickly for one task, and conflict will only occur in the sam e situation, w ith little or no generalization. Teach a subject to th in k about his or h er own thinking in all situations, and generalization is greatest. These results indicate it is possible, although to varying degrees, to accelerate developm ent of a concrete thinker into a m ore form al thinker. Learning Cvcle Studies and A chievem ent R enner and Paske (1977) com pared a learning cycle physics course 46

w ith the traditional lecture class. The learning cycle group had greater content achievem ent gains, had greater satisfaction w ith instruction, and made greater gains on the W atson-Glaser critical thinking m easure. R esults were mixed on reasoning ability. Concrete students b e n ^ te d m ore from learning cycle instruction th an traditional form al instruction w hile th e lowlevel form al students benefited from both forms of instruction. The relevance of this study stem s form the direct application of a learning cycle to physics instruction. The findings of increased reasoning ability and increased content achievements are supportive of using a learning cycle treatm ent. P urser and R enner (1983) examined th e influence th a t one hour of exposition versus learning cycle has upon 8th/9th grade achievem ent of concrete and form al concepts. They found th e learning cycle group scored significantly higher (p < .001) on concept achievem ent of biology concepts which are concrete th a n did the exposition group. There were no significant differences betw een groups on concept achievem ent of biology concepts which are formal. T hus, when teaching form al concepts to 8 th or 9 ih grade students, th e instructional practices do n o t m atter because stu d en ts in th is grade level do n ot achieve conceptual understanding of form al concents. These conclusions apply directly to the type of concepts th a t should be p art of learning cycles. Saunders an d Shepardson (1984) exam ined the effect of form al versus concrete instruction upon science achievem ent and th e reasoning ability of sixth grade students. Form al instruction used lectures, discussions, w ritten and reading assignm ents, films, quizzes, and exams. No laboratory was implemented for th is group. Concrete instruction made use of th e learning cycle. Both treatm en ts w ere implemented for nine m onths. S aunders and Shepardson (1984) found th e concrete instruction group had a significantly (p < .01) higher p o sttest and delayed posttest science achievem ent score 47

than the form al instruction group had. In addition, th e concrete instruction group had more increased reasoning ability th a n the form al group. Learning Cycle Studies and Undergtanding/Meaningfiil Understanding Since learning cycles improve reasoning ability, it follows th a t better reasoners should have greater understandings. Note these studies don’t necessarily exam ine meaningful understanding. Schneider and Renner (1980) exam ined 9 th grade physical science students’ understanding and reasoning. One group received one hour of exposition w hile th e other group received one h our of learning cycle. Both treatm en ts lasted for 12 weeks. The learning cycle group outscored th e exposition group on content achievem ent. F u rth e r statistical analysis revealed th a t neith er IQ nor reasoning abUity was responsible for the significant difierences found between th e treatm ents. In addition, the learning cycle group showed greater gains in reasoning ability th an the exposition group. These gains were also retained over th e reasoning ability postrposttest adm inistered th ree m onths after treatm en t. Stepans, Dyche, and Beiswenger (1988) com pared th e effectiveness of eq) 08itory instruction and learning cycle instruction in prom oting improved understanding about sinkmg/floating concepts in students enrolled in a science class for elem entary education m ajors. R esults of interview s revealed n either group had more than 60% of th e answ ers w ith explanations correct. The auth ors explained th a t this m ay be due to th e problems reported teaching form al concepts to concrete operational students. Both eaqx)sition and learnin g cycle improved the college stu den ts’ understanding of sinking/floating concepts. However, the learning cycle group had a higher percentage of correct responses th an the expository group. They suggest using the learning cycle to teach science concepts for w hich students typically exhibit misconceptions. This is because to rid oneself of 48

misconceptions, one m u st interconnect various ideas, concepts, or events. Once a student exam ines these w ith reference to one another, he or she m ust either accommodate or reorganize in order to resolve the m ism atch un­ covered. Such a process was described as m eaningful learning (Dickie, 1994). Lawson and W eser (1990) exam ined the degree to w hich nonscientific beliefs about life (creationism , orthogenesis, the soul) were held in comparison to reasoning level. The sam ple consisted of university, nonm iyor, biology students. The learning cycle w as used in th e laboratory section of th e course. They found th a t stu den ts w ith higher reasoning ability tended to move aw ay from misconceptions about life tow ard valid conceptions and understanding. Thus, the learning cycle could be said to improve conceptions also. Meaningful understanding is often described as having valid conceptions, not misconceptions. M arek and M ethven (1991) exam ined the students o f teachers who completed a science in-service workshop designed to teach teachers th e use of the learning cycle. They com pared th eir students to th e stu d en ts of teachers who did not com plete th e in-service and who tau g h t by exposition. They examined th e elem entary students’ conservation reasoning as m easured by P iagetian conservation task s and th e language th ey used to describe several objects. They found the students in learning cycle classes had significantly (p = .05) g reater gains in conservation reasoning th a n th e students in the expository classes. They concluded the im provem ent in conservation reasoning was th e resu lt of learning (ycle experience. The students’ descriptive language statem ents were exam ined qualitatively and quantitatively. They found th e language of students from th e learning cycle classes had higher quality descriptions of objects th a n those given by students from expository classes. In addition, th e former group also had significantly (p < .05) higher gains in the average num ber o f words th ey used 49

to describe th e objects. T hey concluded the gains in th e num bers of descriptive words could be attrib u ted to the learning cycle or th e direct experiences in them . Hence, an understanding of th e scientific concept of property w as g reater in learn in g cycle classes th an in eiqx>sitory classes. M eichtiy (1992) recom m ended the use of learning cycle instruction to promote th e scientific literacy of m iddle school students. She cautioned teachers to sequence learn in g cycle activities to accommodate th e four levels of concept understanding. F or example, a descriptive understanding is necessary for a qualitative understanding. Sim ilarly, a qualitative understanding is necessary for a quantitative understanding which is a prerequisite for symbolic understanding. According to M eichtry (1992) middle school students who are req uired to leam concepts w ith a symbolic understanding before they have th e other prerequisite understandings "often become fru strated by th eir in ab ility to understand th e content and com pensate by m em orizing th e inform ation to appease th e teacher” (p. 440). She claim s th e resu lts of such m em orizing are students w ith poor understanding and w ith decreased motivation. In addition, th e learning cycle fosters more positive attitu d es, increased problem-solving and decision making, as well as improved com m unication and cooperative skills. All of the above are necessary for scientifically literate citizens. T his study is relevant to the proposed study since it found th e learning cycle increased problem solving. The understanding required for problem solving will be a sub­ m easure of m eaningful understanding in the proposed study. Based on this evidence, th e learning (ycle seem s likely to increase th e understanding required for problem solving. M arek, Cowan, and Cavallo (1994) used a learning cycle and an e3qx>sitoiy lecture on diffusion to determ ine th e misconceptions prevalent before and after instruction in th e high school biology students. They found 50

th a t none of th e students had an understanding of diffusion before instruction. However, 94% of th e learning cycle class’s concept evaluation statem ents dem onstrated an understanding of th e diffusion concept while only 58% of th e expository class’ statem ents dem onstrated an understanding. The authors point out th a t in order to understand a concept rath er than to hold on to misconceptions, a connection of related ideas and facts m ust be linked to other known concepts. This stu d y suggests th a t this linkage m ust be m ade by th e student during activity such as learning cycles, not by th e teacher during exposition. The authors point out th a t 58% of the expository class did, however, m ake the connections to allow them to understand the concept of diffusion. Why or w hat is it about these students th a t allowed them to m ake th e transition from m isunderstanding to understanding? The authors suggest th a t fu rther research into meaningful learning orientation be conducted to test th is hypothesis. Sunal, e t al. (1992) described a K-8 curriculum about n atu ral resource science. I t was "designed to address the concerns w ith th e environm ent and stew ardship of th e planet via teaching of higher order th o u ^ t processes, and fostering m eaningful learning” (p. 1). The learning cycle approach was the chosen procedure. Concept m aps were also a p a rt of th e curriculum . This was the only study found in th e literature th a t associated th e learning qycle and meaningful learning. However, no research studies of th e effects of this curriculum were reported to substantiate th eir claim of m eaningful learning.

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CHAPTER 3 Methodology

A quasi-experim entai design using a non-equivalent control-group was used in this research. Such a design is characterized by the non-random assignm ent of subjects to groups and the adm inistration of pretests and posttests to each group. P retests and p osttests of students’ reasoning ability, their meaningful learning orientation, and th eir m eaningful under­ standing was adm inistered to each group. In th e following text, LC represents th e learning cycle treatm ent and MVRL represents the meaningful verbal reception learning treatm ent. Sample The sam ple consisted of college students enrolled in two sections of an algebra-based, first sem ester, freshm en level, physics course. In itial to tal enrollm ent in th e two sections combined w as norm ally about eighty students. The class m et three hours per week for "lecture” and two hours per w eek for "laboratory” for 16 weeks. The sample was from a university in th e M idwest having an enrollment o f3500-4500 students. The university serves a somewhat ru ral com m unity. The city in w hich the university is located has a population of about 18,000. One of th e two sections was random ly chosen to receive th e learning cycle treatm ent, while th e other section received th e meaningful verbal reception learning tre a tm e n t Because of conflicts w ith stud ent schedules, it was not possible to random ly assign individual students into treatm ent groups. S tatistical m ethods should elim inate any initial differences betw een the two groups due to non-random ization. Previous departm ental analyses of the two sections over th e p a st six years has n o t yielded any mcgor differences 52

in students’ academic achievem ent between the two sections. The researcher ta u g h t both sections of th e lectures and all labs which minimized any effect of teacher variable. This researcherA nstructor is an assistant professor of physics w ith a m asters degree in physics. She has taught the course prim arily as a lecture (3 hrs) and laboratory (2 hrs) course for ten years and h as received very good evaluations from both students and adm inistrators. Instructional Treatments Physics concepts tau g h t w ere th e sam e for each treatm ent. Students were instructed in th e traditional topics typically tau g h t in G eneral Physics L motion, forces, work, miergy, momentum, circular motion, gravitational law, Archimedes’ Principle, density, Pascal’s principle, pressure, heat, phase changes, linear expansion, and the gas laws. The learning cycle (LC) activities allowed the stud en ts to in teract w ith m aterials th a t provide th e data which they used to form ulate th e ir own concept. In theory, learning cycles allow students to le a m concrete and formal concepts only if th e students are in transition betw een intuitive and reflective thinking or are completely reflective thinkers. D escriptive and empirical-abductive learning çycles were modified or w ritten for use in the learning cycle treatm en t. Learning cycle explorations took place in the laboratory section w ith occasional explorations during th e "lecture” tim e because of the g reater num ber of lecture periods a week. Som etim es these e^ lo ratio n s were carried out in th e classroom and other tim es a laboratory room was available for stu d en t use. The "lecture” tim e w as used for conceptual invention (if n ot completed in lab), expansion of th e concept activities, or testing. Appendix C contains the learning cycles used in the LC treatm ent. Expansion of the idea activities often were problem s from College

Physics., 4th edition by Serw ay and Faughn (1996) and problem s given by ffie 53

instructor. Note th e treatm en ts w ere num erically coded for analysis. In MVRL, students w ere tau g h t how to construct concept m aps from the ideas presented in Learning How to Leam by Novak and Gowin (1984). MVRL students covered th e sam e m aterial as the LC group, however it was covered in a different order. Topics and concepts were taug ht from th e m ost general (energy and m atter) to th e m ost specific (i.e. acceleration and specific heat) according to A usubel who stated th a t students m ust have m ore general knowledge initially to w hich m ore specific knowledge can be attached (subsum ption). S tudents w ere given inform ation about th e various concepts from the researcher through verbal instruction, advance organizers, and th e textbook College Physics., 4 th edition by Serw ay and Faughn (1995). S tudents then organized th is inform ation w hen they constructed concept m aps. For example, MVRL stu d en ts were given assignm ents such as, * ^ a d pages 303 to 305 and construct a concept m ap on therm al expansion”. The MVRL laboratories were also ta u g h t using concept maps and advance organizers even though a trad itio n al lab book (Weems (1990)) w as used. Appendix D contains concept m aps th a t guided study in the course (done by researcher) and a sam ple of stu d en t concept maps. T hree concepts w ere chosen for analysis in this study: forces, Archimedes’ Principle/density, and heat. O f course, a g reat m any more concepts w ere covered in th e course. All topics in the course were tau g h t according to the prescribed trea tm en t so students were accustomed to th e treatm en t style.

V ariables and D ata Analysis The variables of th e stu dy w ere categorized by research questions and are described below. D escriptions of th e d ata analysis are provided for each question. 54

Question 1: W hat are th e m agnitude and direction of any m easurable significant difierences in m eaningful understanding of physics concepts and meaningful learning orientation between students w ifh learning cycle instruction and those w ith m eaningful verbal reception learning instruction? F irst, the question about difierences on m eaningful understanding was addressed. The learning cycle treatm ent (LC) was one independent variable of the study and the m eaningful verbal reception learning treatm ent (MVRL) w as also an independent variable. The reasoning abilities of the leam ers, th eir prior knowledge, and th eir m eaningful learning orientation were covariates for th e determ ination of difierences on m eaningful understanding. The dependent variable was the students’ m eaningful understanding and allowed the exam ination of treatm ents as covariates significantly altering students’meaningful understanding. In order to determ ine if any difierences exist between the LC treatm ent and th e MVRL treatm en t on th e m eaningful understanding variable, an analysis of covariance (one-way ANCOVA) was used. The efiects of students’ reasoning ability, prior knowledge, and meaningful learning orientation (all p retest m easures) w ere covaried so th a t their efiect upon their m eaningful understanding was controlled. In this way any significant difierences betw een th e groups w ere attrib uted to the treatm ent (LC or MVRL). Also, the ANCOVA adjusted for any initial difierences between groups on m easured variables present because of non-random ized samples. However, if there were no initial difierences betw een the groups and there w ere no efiects on m eaningful understanding because of reasoning ability, prior knowledge, or m eaningful learning orientation, then the statistical analysis became a simple one-way analysis of variance. A ttrition caused the two groups to have unequal num ber of m em bers in two of the concepts 55

tested, so one member from one group was random ly removed from th e larger sam ple to use the ANCOVA m ethod of analysis which required equal groups. Thus, forces sample had 25 members for each treatm ent, while th e density/Archimedes’ Principle and h e a t samples had 24 members for each treatm ent. Non-norm ality of d ata w as not a problem because th e ANOVA and ANCOVA were robust to th e assum ption of norm ality. In o ther words, only large departures from norm ality would force nonparam etric m easures to be used. Next, the question about differences in students’ m eaningful learning orientation was addressed. The reasoning abilities of th e leam ers and th eir prior knowledge were covariates for th e determ ination of differences on meaningfrd learning orientation. These covariates w ere m easured so any effect they m ight have were controlled statistically w ith respect to th e independent variable of concern (LC or MVRL treatm ents). The dependent variable was the students’ m eaningful learning orientation. This allowed the determ ination of w hether or not th e treatm ents significantly alter students’ m eaningful learning orientation. In order to determ ine if any differences exist between th e LC and MVRL treatm ents on th e m eaningful learning orientation variable, a one­ way ANCOVA was used. The effects of students’ reasoning ability and their prior knowledge (pretest m easures) w ere covaried so th a t any significant differences in m eaningful learning orientation (dependent variable) between the groups were attributed to the treatm ents (LC or MVRL). However, if there were no initial differences between the groups and there were no effects on m eaningful learning orientation because of reasoning abilify and prior knowledge, then th e statistical analysis becomes a sim ple one-way ANOVA.

56

Q uestion 2: W hat are the m agnitude and direction of any m easurable significant differences in meaningful understanding of physics concepts as m easured by the: (1) conceptual questions, (2) problem-solving, and (3) m ental models betw een students fi*om th e LC and MVRL groups? This p a rt of th e study determ ined, for example, if th e LC treatm en t improved stu d en ts’ scores on problem solving more th an th e MVRL treatm ent. The procedure wUl be m uch th e sam e as was done in question one, except th a t it m ust he done for each of th e th ree m easures of understanding. The LC and MVRL are independent variables of the study. The learn ers’ reasoning abilities, ih e ir prior knowledge, and th e ir meaningful learning orientation are covariates for the determ ination of difierences on each individual m easure of m eaningful understanding. The dependent variable, stu den ts’m eaningful understanding individual subscores, w ill allow the exam ination of treatm ents as covariates altering students’ meaningfiil understanding on an individual m easure of meaningful understanding. A one-way ANCOVA was used to determ ine if any difierences exist between the LC and MVRL treatm ents on th e m eaningful understanding as m easured by each instrum ent. The efiects o f students’ reasoning ability, prior knowledge, and meaningful learning orientation (pretest m easures) can be covaried so th a t th e ir efiect upon th eir m eaningful understanding on one m easure can be controlled. In this way any significant differences between the groups can be attrib u ted to th e trea tm en t (LC or MVRL). Q uestion 3: W hich variable- reasoning ability, meaningful learning orientation, prior knowledge, or instructional treatm ent—is the best predictor of overall m eaningful understanding of physics concepts? To determ ine w hich variable best explained students’ overall meaningful understanding of physics concepts, a stepw ise m ultiple regression w as perform ed w ith students’ reasoning ability m easured by th e TOLT, th e ir m eaningful learning 57

orientation m easured by th e LAQ, prior knowledge m easured by th e overall physics understanding score, and instructional treatm en t (LC or MVRL). These variables w ere entered as predictor variables in th e regression analysis. Q uestion 4: Which variable—reasoning ability, m eaningful learning orientation, prior knowledge, or instructional treatm ent—is th e best predictor for each sub-m easure of m eaningful physics understanding? To determ ine which variable best explained students’ sub-scale m eaningful understanding of physics concepts, a stepwise m ultiple regression was perform ed w ith students’ reasoning ability m easured by th e TOLT, th eir m eaningful learning orientation m easured by th e LAQ, prior knowledge m easured by th e overall physics understanding score, and instructional treatm en t (LC or MVRL). Four variables w ere entered in th e regression analysis to predict stu d en t understanding on th ree understanding m easures. These variables were (1) high level conceptual questions, (2) problem-solving, and (3) m ental model scores. For exam ple, the regression analysis allowed the determ ination of th e variable m ost im portant for th e understanding required for problem solving. M easures Reasoning Abilitv Measure All of th e instrum ents m ay be found in ^ p e n d ix B. T he T est of Logical Thinking (TOLT) was used to determ ine th e students’ reasoning ability. The TOLT is a 10 question instrum ent m easuring form al or reflective reasoning. E ach item requires th e correct response and justification for the response. Scores on th e TOLT range from 0 to 10. The reliability of th e TOLT was reported as .85 and th e internal consistency w as reported as ranging from .56 to .82 for each two p art su b test (Tobin & Capie, 1981). The predictive validity of the TOLT w as reported as .74, while th e criterion 58

validity betw een th e TOLT to Piagetian interview was .80 (Tobin & Capie, 1981). Meaningful Leaminy O rientation M easure The L earning Approach Q uestionnaire (LAQ) is a L ikert scale instrum ent th a t w as used to m easure students’ approach to learning and th eir view of science (Entw istle & Ramsden, 1983; BouJaoude, 1992; Cavallo & Schafer, 1994). This study used only those item s th a t queried stu dents on th eir approach to learning. The higher th e score on the LAQ, the more meaningful is th e stu dent’s approach to learning. Likewise, th e lower th e score, the m ore th e student’s tendency is tow ard rote learning. The LAQ was given as a p retest m easure of students’ m eaningful learning orientation, as has been done by Dickie (1994), and as a posttest m easure of stud ents’ m eaningful learning orientation. The Cronbach-alpha internal consistency for the LAQ has been reported as .77 (BouJaoude, 1992). The sp lit h alf internal consistency w as found to be .71 for data from a previous study (Williams & Cavallo, 1995). Meaningful UnderstandingMeaaure The stu den ts’ m eaningful understanding of physics topics was m easured using high level questions, problem solving, and m ental model scores. Cnnreptiial understanding. Okebukola (1990) found th a t m eaningful understanding m ay be assessed through th e use of m ultiple choice questions th a t are a t th e comprehension level and above. For his research, he used a 40 item te s t in which "40% of th e item s for each te st w ere a t the com prehension level, 30% a t th e application level, 10% a t the analysis level, and 5% a t th e synthesis level, and 5% a t th e evaluation level” (Okebukola, 1990, p. 496). Dickie (1994) has exam ined physics assessm ents previously. Therefore, th is 59

researcher relied upon his categorizations to modify and create a m easure suitable for m easuring m eaningful understanding of physics concepts. The conceptual tests w ere given as a p retest and as a posttest m easure a t th e end of the conceptual unit. The forces te s t of conceptual understanding used w as th e Force Concept Inventory (H estenes, W ells, and Swackhamer, 1992). The FCI is one of the m ost widely used in stru m en ts in physics. The FC I is a 29-item m ultiple choice instrum ent designed to identify Newtonian physics misconceptions. The KR reliability for th e FCI was .86 for th e pretest and .89 for the posttest (H estenes, W ells, and Swackhamer, 1992). The face and content validity of th e item s have been established by th e authors as well. Q uestions 20 and 21 were om itted fi*om th e FCI as the stu den ts found th e questions confusing and the sp lit-h alf reliabilify was found to be r =.744 for th is 27 question version of th e FCI. As far as th e percentages on Bloom’s scale, 18.5% of the questions w ere a t the comprehension level, 44.4% were a t th e application level, 18.5% w ere a t th e analysis level, 11.1% a t the synthesis level, and 7.4% a t th e evaluation level. A 17 question m ultiple choice exam on Archimedes’ Principle and density was constructed to assess h eat conceptual understanding. The splith a lf reliability was .768. On Bloom’s scale, 11.8% were a t th e com prehension level, 23.5% a t th e application level, 35.3% a t th e analysis level, 11.8% a t th e synthesis level, and 17.6% a t th e evaluation level. A 17 question m ultiple choice exam on h eat was constructed to assess h ea t conceptual understanding. The h eat split-half reliability was found to be .823. It was found th a t 23.5% w ere a t th e comprehension level, 29.4% a t th e application level, 23.5% a t the analysis level, 5.9% at the synthesis level and 17.6% a t the evaluation level of Bloom’s taxonomy.

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Prnhlem aolviny. S tudents’ m eaningful understanding of physics problem solving was m easured by tb eir score on a p retest exam and a posttest exam on solving novel problems. Dickie (1994) stated problem s th a t are unfam iliar to th e solver, b u t are structurally sim ilar to fam üiar ones can be used to m easure m eaningful understanding of physics. Since problems are typically given for exams in th e course, six sim ilar problems were chosen to assess tb e ir problem solving understanding. The force exam spU t-balf reUabUity w as .635, the A rcbim edes/density reUabUity was .834, and the b eat reliabUity w as .740. M ental models. Cavallo and Schafer (1994) describe m ental models as an open-ended assessm ent method th a t reveals stu d en t understanding. Students were asked to w rite everything th a t they knew about th ree physics topics: forces, density and Archimedes’ Principle, and beat. Students’ papers were examined for correctness only after being num bered to make them anonymous to the scorer. The original stud en t sheets contained tb e ir nam es since th e correctness of the essays counted as p art of tb eir exam (for posttest only). Only correct inform ation w as used in th e scoring analysis for m ental models. This inform ation from stu d en t sheets was transferred by band onto tem plates sim ilar to th a t used by M osentbal and K irscb (1992). A tem plate is found in Appendix B. Each sentence was transferred to one line of the grid w ith the categories: agent, action, object, receiver, goal or e}q)lanation, effect (points of reference), and tim e, location, and condition (points of observation). M osentbal and K irscb (1992) suggest th a t the growth in understanding of a student can be m easured using a single knowledge model (m ental model) of one concept or topic. The more categories, details in each category, and relationships th a t are included in a m ental model indicate greater m eaningful understanding of the topic th a n 61

when fewer of these item s are included. The m ental model tests were scored by the researcher based upon a num erical assessm ent of categories. Scores may range from zero (no understanding) to some integer (more m eaningful understanding). T his integer may vary on different m ental models topics for some physics topics have greater detail, more c a t^ o rie s, and more linkages than other physics topics. The m ental model m easures w ere also given as a pretest and a p o sttest m easure. One point w as given for each cat% ory included in th e model per sentence. (Note th a t th is is not th e traditional m ental model m ethod of scoring.) For example, if a stu d en t said, ‘ih e ball h it the tree when I threw iff, th e “ball” would be considered th e agent, “hitT the action, “tree” th e object, and the condition “w hen I threw itT; thu s a stu d en t would be given a score of four for th a t sentence. One very common response: “for every action th e re is an equal and opposite reaction”; the condition category contains “for every action”, th e effect category contains “th ere is an equal and opposite reaction force”. Thus, th is sentence would get a score of 2. Two physics teachers unfam iliar w ith the m ental models checked the placem ent of item s into categories for a sam ple of students. Once on th e tem plates (anonym ous once placed on the tem plates), th e tem plates were checked th ree tim es by th e researcher over a period of m onths to ensure uniform ity of placem ent of like and sim ilar item s. A student’s overall physics understanding score w as obtained by summing th e stu d en t’s conceptual question score, problem solving score, and m ental model score. T his overall score was obtained for p retest and posttest. P retest scores w ere used as covariates or as m easures of prior knowledge.

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CHAPTER 4 Results S tatistical analyses were performed to answ er th e four research questions. This chapter will provide the results of these analyses and will be organized by research questions 1 -4 . D escriptive statistics and correlations are in Appendix E. Significance level was taken to h ep < .05 throughout. Question 1

What are the magnitude and direction of measurable significant differences in meaningful understanding of physics concepts and meaningful learning orientation between students with learning cycle instruction and those with meaningful verbal reception learning instruction ? Three one factor analyses of covariance (ANCOVA) were performed to answ er each p a rt of question one for each of th e th ree concept areas tested (forces, density/Archim edes’ Principle, and heat). Note th a t one ANCOVA was performed for forces, one for density/Archimedes’ Principle, and one for heat data to m easure differences in meaningful understanding and in meaningful learning orientation. The results are found in Tables 1 through 6. The independent variable is in bold type. The o ther variables are covariates.

Table 1: Force D ata ANCOVA

Source

df SumofSquares Mean Square \F-ratioi\ P-value

T re a tm e n t 1 Learning ^ p r e a c h i 1 Reasoning A bility 1 Force Understanding! 1 Error 45

1412.314 15.477 20.487 4.900 19622.498

1412.314 15.477 20.487 4.900 436.056

I 3.2391 1 .0 3 5 7 i .047 1 1 O il 1

(dependent variable = overall force understanding)

63

.079 .851 .829 .916

Table 2: Densily/Ârchim edes’ Principle D ata ANCOVA

Source

d f \ Sum of Squares I Mean Square F-ratU>:P-value

T re a tm e n t Learning ^ p ro a c h Reasoning Ability D ensity U nderstanding Error

1 I 1 i 1 i 1 i 43;

546.494 57.937 73.643 192.151 8186.185

546.494 57.937 73.643 192.151 190.376

2.8711 .304 1 .387 1 1.009 I

.097 .584 .537 .321

(dependent variable = overall denaity/Archimedes’ Principle understanding)

Table 3: H eat D ata ANCOVA

Source

d f 1SumofSquares\MeanSquare\ F-ratio IP-value

1 T re a tm e n t 194.368 L earning Approach 1 356.160 Reasoning Ability 1 118.665 H eat U nderstanding 1 1.970 Error 43 I 10361.030

194.368 356.16 118.665 1.970 ! 240.954

i .807 i .374 i 1.478 i .231 I .492 i .487 .008 i .928 1

(dependent variable = overall beat understanding)

Table 4: Force D ata ANCOVA

Source

i df ISum ofSquaresl Mean Square F-ratio P-value .600 T re a tm e n t ; 1 | 10.484 [ 10.484 .279 Reasoning Ability | 1 ] 325.427 | 325.427 .005 8.667 3.094 .085 Force U nderstanding i i 116.168 1Ï6.168 E rror i 4 6 1 1727.277 37.550 (dependent variable = meaningful learning orientation)

Table 5: Density/Archim edes’ Principle D ata ANCOVA

Source

d f \Sum of Squares IMean Square F-ratw\ P-value

1 T re a tm e n t Reasoning Ability 1 D ensity U nderstanding 1 1 Error 44 1

1.696 78.374 78.267 1596.911

.047 i .830 2.159 1 .149 2.157 : .149

1.696 78.374 78.267 36.293

(dependent variable = meaningful learning orientation)

Table 6: H eat D ata ANCOVA

Source

d f\ Sum of Squares Mean Square \F-ratio\ P-value

T re a tm e n t Reasoning Ability H eat Understanding! Error

1 1 1 i 1 I 441

78.325 213.000 56.293 2568.680

78.325 213.000 56.293 58.377

i 1.342 1 .253 1 3.649 1 .063 I .964 1 .331 1

(dependent variable = meaningful learning orientation)

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Table 1 shows th a t the stu d en ts from th e two treatm ents did no t significantly (.05 level) differ in th e ir overall m eaningful understanding of forces (conceptual question score + problem solving score + m ental model score). However, th e learning cycle class had higher overall m ean m eaningful understanding force scores. T he learning cycle class m ean w as 58.511, w hile th e m eaningful verbal reception learning class m ean was 47.649. Sim ilarly, Table 2 shows th a t th e students from th e two treatm en ts did not significantly differ (at th e .05 level) in th e ir overall m eaningful understanding of density and A rchim edes’ Principle. As w ith forces, th e LC treatm en t had higher num erical scores th a n th e MVRL trea tm en t since th e overall m ean density/Archimedes’ Principle m eaningful understanding score was 34.450 while the MVRL stu d en ts’ m ean score was 27.425. Table 3 shows th a t th e LC and MVRL stud en ts did not significantly differ in th eir overall meaningful understanding of heat. Thus, from these analyses, th e answ er to the first p a rt of th e Q uestion 1 is th a t there were no m easurable significant (a t th e .05 level) differences found between LC and MVRL instruction in the stu d en ts’ overall m eaningful understanding of these th ree physics topics. Table 4 shows th a t the treatm en ts for force concepts did n o t differ significantly in their affect on th e students’ m eaningful learning orientation. The MVRL students’ m eaningful learning orientation m ean (66.707) w as only slightly h i^ e r th an th a t of th e LC students’ (65.773). Table 5 also shows th a t th e LC and MVRL students did n ot differ significantly in meaningful learning orientation for th e densify/Archimedes’ Principle concept. Once more, th e MVRL students’ learning orientation m ean (65.737) w as only slightly higher th a n th a t of th e LC students’ (65.346). Table 6 illustrates the sam e lack of difference in treatm en t effect. However, this tim e, the LC students’ m eaningful learning orientation m ean 65

(68.098) was slightly higher th an the MVRL stu d en ts’ m ean (65.402). Thus, for all topics studied, th e LC and MVRL treatm en ts did n o t differ significantly in th eir ability to change th e students’ m eaningful learnin g orientation.

Question 2.

What are the magnitude and direction of measurable significant differences in meaningful understanding of physics concepts measured by (1) conceptual questions, (2) problem-solving, and (3) mental models between IC students and MVRL students? T hree ANCOVA’s were performed to answ er each p a rt of Question 2 for each of th e th ree topics tested (forces, density/A rchim edes’ Principle, and heat). Note th a t th ree ANCOVAS were perform ed for forces, density/Archim edes’ Principle, and h eat to m easure dififerences in meaningful understanding in term s of the sub-m easures of understanding: concept, problem solving, and m ental model. The resu lts are found in Tables 7 ,8 and 9 below.

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Table 7 ANCOVAS from Force D ata

Source T re a tm e n t Concept Score Reasoning A bility i Learning Approach E rror

d f I Sum of Squares Mean Square i F-ratio P-value 1 ; 8.176 \ 1.313 8.176 .268

1 ; 140.898 ! 22.627 .000 140.898 r 9.151 .004 56.980 56.980 i ..! .015 I .002 .015 .962 1 I 6.227 45! 280.208 Source d f ! Sum of Squares i Mean Square \F-ratio\ P-vahte 8.946 1 1 3.236 I .079 8.946 T re a tm e n t .029 Problem Score : .010 1 .919 .029 1 21.890 ! 7.918 ! .007 Reasoning A bility i 1 21.890 Learning Approach! 1 .078 ! .028 1 .867 .078 2.765 E rror 45 124.409 Source d f\ Sum of Squares 1MeanSquare iF-ratio\P-value ! 1226.836 i 2.966 .092 1226.836 T re a tm e n t 1 1 1 .631 ^ .431 260.915 Model Score 260.915 1 1 52.979 ! .128 .722 Reasoning A bility I 1 i 52.979 77.107 Î .187 Learning Approach! 1 ! .668 77.107 413.274 E rror 45! 18597.318 (dependent variable = specific understanding type; Le. concept, problem, model)

Table 8 ANCOVAS from Density/Archimedes’ D ata

Source

df\ SumofSquares ! MeanSquare F-raHdP-value

1 ! T re a tm e n t Concept Score 1 1 Reasoning Ahiiiiiy | 1 1 Learning Approach! 1 ! E rror 43

17.604 43.460 37.485 5.459 348.354

17.604 43.460 37.485 5.459 8.101

! 2.161 ! I 5.365 i ! 4.6271 ! 0.6741

T re a tm e n t 1 ! Problem Score 1 ! Reasoning A bility 1 1 i Learning Approach! 1 ! E rror 43!

21.740 8.240 1.118 5.252 114.077

21.740 8.240 1.118 5.252 2.653

! 8.196 i .006** ! 3 .1 0 6 1 .085 ! .422 ! .520 11.980 ! .167

173.462 22.115 3.772 13.116 7058.008

173.462 22.115 3.772 13.116 164.140

1 1 T re a tm e n t Model Score 1 1 Reasoning A bility i 1 i Learning Approach! 1 1 E rror \ 43 i p < .005 (dependent variable s

I

1.067! 135 ! ! .023 i 1 .080 ! i I 1 1

.149 .025 .037 .416

.310 .715 .880 .779

specific understanding type; Le. concept, problem, model)

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Table 9 ANCOVAS from H eat D ata Source d f\ SumofSquares 1 MeanSquare T re a tm e n t .161 .161 1 i 3.122 3.122 Concept Score 1 I Reasoning Ability 1 1 1 10.676 10.676 12.034 Learning Approach 1 i 12.034 Error 260.755 6.064 43 I 'ï " T T re a tm e n t Problem Score 1 : Reasoning Ability 1 1 i Learning Approach 1 1 Error 43 i

T re a tm e n t 1 ; Model Score 1 I Reasoning Ability ! 1 1 Learning Approach 1 i Error 43 i * P < .05 (dependent variable =

Î ï:0 8 7

;

.862 7.073 .279 79.974

ÎÎ.0 8 7 .862 7.073 .279 1.860

153.395 22.140 304.103 209.914 8971.703

153.395 22.140 304.103 209.914 208.644

\F-ratid\P-value 1 .027 i .515 I Ï.761 1 1.984

1 : 1 ;

.871 .477 .192 .166

: 5 .9 6 1 1 I .464 1 1 3.803 i 1 .150 1 1 1

.019* .500 .058 .700

: .735 I .106 1 1.458 : 1.006

I .396 .746 .234 .321

I 1 i

specific understanding type; Le. concept, problem, model)

Table 7 shows th e ANCOVAS for the dependent variable of meaningful understanding of forces when the understanding score is eith er a conceptual, a problem solving, or a m ental model understanding score. From Table 7 it is apparent th a t th e students’ force concept scores, th eir problem solving scores, or th eir m ental model scores did not differ significantly according to treatm ent. In other words, students in a LC class did not have significantly better problem solvers or better concept understanding or better m ental model builders th an those in the MVRL treatm ent, and viceversa. Though the differences were not significant a t the .05 level, they w ere significant a t the .1 level for problem solving and m ental models. In both cases, th e LC presentation of forces created a slightly higher m ean problem solving score (3.344) and m ental models (42.251) th a n did th e MVRL treatm ent on forces ( 2.456 and 32.229, respectively). Table 8 shows the ANCOVAS for the dependent variable of 68

meaningful understanding of density/A rchim edes’ Principle when the understanding score used is either a conceptual, a problem solving, or a m ental model score. T his tim e the analyses w ere mixed. There were no significant differences in th e students’ conceptual and m ental model building understanding of density/Archim edes’ P rinciple between the LC and MVRL treatm ents. A lthough in both cases th e LC stu d en ts had slightly greater m ean scores in both areas com pared to th e MVRL students. However, th e LC and MVRL students did significantly differ in th eir problem solving. The LC students had a g reater m ean understanding in density/Archim edes’ Principle problem solving th an did th e MVRL students. The LC problem solving m ean w as 4.079 w hile th e MVRL trea tm en t m ean for problem solving was 2.587. T hus, th e m agnitude of th e difference was 1.492, or roughly 1.5 problems w hich represents a 25% im provem ent over th e MVRL treatm en t m ean. Table 9 shows th e ANCOVAS for th e dependent variable of meaningful understanding of h eat w hen th e understanding score used is eith er a conceptual, a problem solving, or a m ental model score. As w ith density, the results w ere mixed. T here w ere no significant differences in the LC versus the MVRL treatm en ts in conceptual and m ental model understanding. However, th e LC and MVRL treatm ents were significantly different in problem solving understanding (p = .019). However in th is case, the MVRL were greater problem solvers th a n did th e LC students. The MVRL problem solving m ean was 2.736 w hile th e LC problem solving m ean was 1.764. Thus, th e m agnitude of th e difference w as .972, or alm ost one problem greater w hich represents a 16% im provem ent over the LC treatm en t m ean. Hence, ih e answ er to Q uestion 2 is complex. Based upon th is research, if forces was th e topic being studied, it m ade no difference which 69

treatm ent (LC o r MVRL) was used. The understanding was not significantly difierent. U nderstanding scores on concept tests, problem solving, and m ental models w ere practically th e same. However, if density/Archimedes* Principle w as the topic being studied, the results of th is research dem onstrates th a t th ere was no significant difference betw een th e treatm ents in term s of producing concept and m ental model understanding. However, a 25% im provem ent in problem solving over th a t by th e MVRL group was made by th e LC g ro u p . Recall also th a t th e students in ihe learning cycle treatm ent also had slightly higher m eans (although not significant) on concept and m ental model understanding m easures. T hus, th e LC treatm ent was b etter a t producing understanding in problem solving w hen density/Archimedes’ Principle was the topic studied. W hen h e a t w as th e topic studied, th e MVRL treatm en t was 16% better th an th e LC treatm ent a t producing understanding in problem solving. Also, th e stu d en ts in th e MVRL treatm ent had slighUy higher m eans (although not significant) on conceptual and m ental model understanding. Thus when th e topic being studied was h eat, a MVRL treatm en t was b est a t producing understanding in problem solving.

Questions. Which variable (reasoning ability, meaningful learning orientation, prior knowledge, or instructional treatment) is the bestpredictor of overall meaningful understanding ofphysics ooncqpts? To determ ine th e variable th a t best predicts students’ overall m eaningful understanding of physics concepts, a stepw ise m ultiple regression was performed w ith reasoning ability (TOLT), m eaningful learning orientation (LAQ), prior knowledge (overall meaningful understanding score which is sum 70

of concept, problem solving, and m ental model scores), and treatm en t (LC or MVRL) entered as predictor variables. For overall m eaningful understanding of th e force concept (posttest), treatm ent was tbe best predictor although it was not significant a t th e .06 level (r = -.263, F = 3.561, df= 48, p = .065) [ r = correlation; F = F statistic;

d f = degrees of fi-eedom; p = probability]. For posttest overall understanding of density/Archimedes’ Principle, treatm en t was the best predictor (r = -. 198,

F - 1.878,

= 46, p = .177). However, it was excluded from th e regression

model since p > .05. Thus, for density, th ere was no significant predictor of overall meaningfiil understanding. For posttest overall meaningful understanding of heat, th e students’ m eaningful learning orientation w as th e best predictor (r = .157, F - 1.155, d f= 46 p = .288). It was excluded from th e regression model since p > .05. Based upon these three findings. Q uestion 3 m ay not be form ally answ ered as none of th e entered variables added any more to the prediction of overall understanding in the regression model. N either reasoning ability, learning approach, prior knowledge, nor treatm en t were significant predictors of overall m eaningful understanding. Therefore, it is not possible to answ er Q uestion 3 from th e data of this study.

Which variable (reasoning ability, meaningful learning orientation, prior knowledge, or instructional treatment) is the bestpredictor for each sub-measure of meaningful understanding of physics ? Three stepw ise m ultiple regression analyses were done for each sub­ m easure (concept, problem solving, m ental model) of m eaningful understanding, h i other words, for concept understanding, a regression analysis was done for forces, density/A rchim edes’ Principle, and for heat. For concept understanding it w as found th a t for forces, prior knowledge 71

(r=.587, F = 21.861,
d f - 46, p = .015). Reasoning ability th us explains 12.1% of th e variance in students’ h e a t concept scores. In sum m ary, students’ conceptual understanding was b est predicted by students’ prior knowledge scores for forces and density/Archim edes’ Principle. However, students’ heat concept understanding w as b est predicted by th e ir reasoning ability. Recall also th a t students’ reasoning ability w as also a significant predictor for force and density/A rchim edes’ Principle conceptual understanding, although it was of slightly lesser im portance in th e regression model. For predicting students’ problem solving score for forces, th e stepw ise m ultiple regression revealed th a t the students’ reasoning ability w as the only significant predictor (r = .391, F = 8.681, df= 46, p = .005). R easoning ability explained 16.3% of th e variance in force problem solving. T reatm en t was th e second stron gest predictor although its probability was slightly g reater th an 72

.05 (r = -.269, F = 3.666 , d f =46j p = .062). N ote th a t for forces, th e n ^ a tiv e on the correlation m eans to be in a LC class indicated higher problem solving posttest scores. For density/A rchim edes’ Principle problem solving, treatm en t w as ih e only significant predictor of students’ problem solving scores (r = -.277, F = 8.283, df= 46, p = .006). This negative correlation m eans th a t being in a MVRL treatm en t correlated w ith decreased problem solving scores. The LC treatm ent correlated w ith increased problem solving scores. T reatm ent e ^ la in e d 7.7% of th e variance in density/Archim edes’ Principle problem solving scores. The students’ reasoning ability was th e b etter significant predictor of heat problem solving (r = .356, F = 6.507 , df= 46, p = .014). T reatm ent w as the next best significant predictor of students’ h ea t problem solving (r = .338,

F = 5.803, df= 46, p = .020). For th e topic of heat, th e positive correlation means th a t being assigned to a MVRL class correlates w ith g reater problem solving scores. T ogether these two variables predicted 22.6% of the variance in heat problem solving scores. Thus, for forces and h eat topics, students’ reasoning ability w as th e most effective predictor of students’ problem solving scores. For h eat topics, treatm ent was the n ex t best predictor of students’ problem solving scores. For density/A rchim edes’ Principle however, treatm en t was the only significant predictor of students’ problem solving. However, th e id e al’ treatm ent varied by topic being studied: densily/Archim edes’ Principle or h e a t Being in a LC class when studying densily/Archim edes’ Principle correlated w ith higher problem solving scores, yet being in a LC class for h eat topics correlated w iA low er problem solving scores. To find the b est predictor of students’ m ental model scores, three stepwise m ultiple lin e ar regressions were performed. None of th e predictor 73

variables (reasoning abiliiy, learning approach, prior knowledge, or treatm ent) w ere significant and entered into the r^ re ssio n model. Thus, it is not possible to gain in sig h t into predicting m ental model scores finm this work.

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CHAPTER 5 Discussion and Conclusions Due to the length of the discussions and the number of research questions, the discussion of th e results and conclusions drawn from these results will be organized by research questions 1 through 4. For example, question 1 will be discussed immediately followed by the conclusions drawn from the results of question 1. Discussion of Question 1: Overall Meaningful Understanding. The ANCOVA results were similar for th e three physics concepts examined. No measurable differences in meaningful understanding (p >.079 and higher) were found for forces, density/Archimedes’Principle, or heat. T h at is, the LC students had virtually the sam e overall meaningful understanding on the three items tested as did the MVRL students. S eparate trtests comparing pretest and posttest scores of overall understanding for each group revealed a significant ip < 000) increase in meaningful understanding of the three physics concepts (Williams, 1997). Therefore, the LC and MVRL college physics students improved th eir meaningfiil understanding of forces, density/Archimedes’ Principle, and heat. W hat does this mean? The students from th e different treatm ents had nearly equal overall (conceptual + problem solving + mental model) meaningfid understandings. Students in this sample were in transition or were reflective (or formal operational) thinkers. The LC and MVRL results were similar because Piagetian and Ausubelian thew ies specified sim ilar criteria for meaningful learning. Both theoriea explain learning b u t in different tprminnlngv. Following are a description of Piagetian theory eiqilaining learning w ithin the LC treatm ent and a description of Ausubelian theory explaining learning in the LC treatm ent. Figure 14 illustrates both 75

theories. Some students in this study were given "physics" experiences th r o u ^ th e learning cycle. According to th e research results, they took this eiqierience, constructed the concepts offerees, density/Archimedes’ Principle, and h eat and formed greater meaningful understanding of these physics concepts. According to Piaget’s (1963) th e o ry , the concrete eiqœrience allowed assimilation (incorporation of experiences into mental structures) which led to disequilibrium (conflict between m ental structures). D uring the conceptual invention phase of the learning çycle, accommodation (change or development of new structures) occurred. Piaget called the processes of assimilation and accommodation adaptation. The student adapted to the input from the exploration. D uring conceptual e ^ a n sio n , the student organized the new m ental structure with structures previously developed. Piaget called this process organization. Thus, the students increased their meaningful understanding of the concept. Ausubelian theory can also be applied to e ^ l a in students’ learning during the LC. In th e Ausubelian interpretation, th e concrete eiq)eriences during the exploration provided th e relevant prior knowledge necessary for meaningful learning. The exploration also provided the opportunity for subsumption during which new information was related to more general ideas, making the ta sk potentially meaningful to th e student. D uring the conceptual invention phase, the researcher encouraged the students to make links between data or observations. Students were also encouraged to orient th eir learning toward meaningful learning rath er th a n rote. Students were encouraged to link new terminology to the phenomena observed during the exploration. In this manner, the students linked other items to th e phenomena, or concept, being studied. Ausubel (1963) called m aking such new links progressive differentiation. During the expansion phase, students 76

related the phenomena w ith the new links and terminology w ith new concepts or ideas. Superordinate learning (new links cause one idea to subsume a previous one) and integrative reconciliation (new links form between the old and new ideas) occurred during the conceptual invention phase of the LC. h i each process, th e learner formed linka between the new ideas and other concepts or ideas for which no links previously existed. P ia g etia n

LC Elxploration

A u su b elian gives prior knowledge subsum ption

assimilation disequilibrium

C oncept In v en tio n i iprogressrve differentiation accommodation C oncept E xp an sion (or a p p lica tio n ) i 1 superordinate learning organization ; integrative reconciliation Figure 14. The learning cvcle and Piagetian and Ausubelian explanations of how each phase led to overall meaningful understanding.

Similarly, each theory can be used to explain how th e MVRL treatm ent led to students’ meaningful understanding. Following are a description of Piagetian theory explaining learning with th e MVRL treatm ent and a description of Ausubelian theory explaining learning in the MVRL treatm ent. Figure 15 illustrates both theories. The MVRL treatm ent had several phases. M aterial was presented through verbal instruction followed by advance organizers. Ideally, the students were to construct concept m aps from th e advance organizers before the laboratories. The students completed laboratories th a t utilized concept maps to introduce the underlying theoiy in the laboratory. More advance organizers, verbal instruction and concept m aps followed th e laboratory.

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According to Piagetian theory (Piaget, 1963), th e students who were in transition or who were formal operational assimilated the input from the verbal instruction. Concrete operational students do not assimilate abstract concepts and require concrete experience. According to Piagetian theory, concrete operational students do not leam formal concepts. However, if concrete experiences w ere provided, they might le a m concrete aspects of the concept. In this study, none of the students were concrete. Therefore, according to Piagetian theory these formal students had the ability to leam formal concepts although they m i ^ t not choose to operate a t a formal level. Thus, th e use of verbal instruction and advance organizers does not prevent the application of Piagetian theory for this sample. However, care m ust be taken when applying Piagetian theory to younger samples who are cognitively less developed. After the verbal instruction, students were told to construct concept maps relating various aspects of the concept(s). The construction of th e concept maps were usually based upon reading passages from the textbook. During the construction of the maps, the students took charge of their own learning. Students struggled with ways to relate th e items in the passages from th e textbook for additional assimilation. The laboratories provided the opportunity for the students to become disequilibrated and to accommodate to the data. Students usually attended laboratories before the concept maps were collected for grading. Therefore, the processes of disequilibrium and accommodation probably occurred in the laboratory rath e r than during the construction of concept maps. The process Piaget called organization occurred as the students read more advance organizers and constructed more concept maps. Organization occurred during th e students’ efforts to construct a concept m ap th a t related their thoughts about additional concepts to their thoughts about the new phenomena or concept studied. 78

According to Ausubel (1963), prior knowledge and subsum ers for concepts were provided by verbal instruction. Students were encouraged to orient their learning away from rote w hen they were asked to construct concept maps. Laboratories and concept maps also promoted subsum ption and progressive differentiation as new links were created. More advance organizers or verbal instruction caused th e students to link items to other, less specific items (superordinate learning according to Ausubel). Furtherm ore, integrative reconciliation was accomplished as additional maps were constructed or revised by the student. P ia g e tia n

MVRL ! v e rb a l in stru c tio m

assimilation*

A u su b elian 1 prior knowledge subsum ption

ad v a n ce o rg a n iz e rs & co n c e p t m a p s assimilation*

subsum ption progressive differentiation la b o ra to rie s

disequilibrium accommodation

subsum ption pr%ressive differentiation ad v a n ce o rg a n iz e rs co n c e p t m a p s

organization

superordinate learning 1 integrative reconciliation

* for formal operational sample only. Figure 15. Meaningful verbal reception learning and Piagetian and Ausubelian explanations of how each phase led to overall meaningful understanding.

Conclusions from Question 1: Overall Meaningfiil Underafainding. College physics students from each treatm ent achieved nearly the same overall meaningful understanding on each of the three physics concepts examined. Piagetian and Ausubelian theoiy can explain how th e students in each treatm ent achieved overall meaningful understanding. I t appears th a t 79

Piaget and Ausubel have viable theories of learning. Piagetian theory can be used to explain meaningful learning in the learning çycle as well as meaningful learning in meaningful verbal reception learning. Ausubelian theory can be used to explain meaningful learning in th e learning cycle as well as learning in meaningful verbal reception learning. The two theories appear to eq)lain learning in difierent terms. More research needs to be conducted to validate this premise. F u rth er research could determine if th e sequence of the phases of MVRL could be altered to obtain better student meaningful understanding. U sually concept m aps were assigned on Mondays, laboratories were on Tuesdays, and concept maps were collected on Wednesdays. Students who procrastinated could have done th eir maps on Tuesday night after the laboratory. I t needs to be determined if the order of these activities in the MVRL sequence is associated with a change in students’ meaningful understanding. One weakness of this study is th a t the order of th e LC concepts was from general to specific within each concept, not course wide. Whereas, this order (general to specific) was followed for th e entire MVRL treatm ent. The LC curricula should be organized so th a t the concepts are covered in order from those th a t are more general to those th a t are more specific. According to Ausubel, this organization should favor meaningful learning, but research should be done to investigate this. Research should be done th a t compares these two treatm ents to the typical college physics lecture^ab treatm ent. The m ajority of college professors will never consider abandoning th eir lecture/lab physics unless statistics indicate g reater success by using one or both of these curricula. Discussion of Question 1: Meaningfiil Teaming Orientation The rem aining p a rt of Question 1 is th e meaningful learning 80

orientation of th e students in the two treatm ents. Recall th a t for forces, density/Archimedes’ Principle, and h eat data, the LC and MVRL students’ meaningful learning orientation did not differ significantly. Could it be th a t students fix)m each treatm en t were draw n away fix>m rote m eans of learning by roughly the sam e significant amounts? This was not th e case in this study. Ad hoc t-tests showed th a t there was not a significant change in meaningful learning orientation scores (pretest to posttest) for either treatm ent. N either group of students increased or decreased their tendenqr to leam meaningfully. This was a single four-hour, sixteen-week course in the students’ college career. Perhaps this is evidence th a t it is n o t possible to change the learning orientation of college physics students during such a short trea tm en t A shift in learning would possibly be observed if the course was offered over a longer period of time, if all science courses th a t students have taken previously were taught in th e sam e manner, or if all instructors taught using procedures th a t do not rew ard rote learning. Conclusions from Question 1: Meaningfiil team ing Orientation Students in th is study from the LC group did not alter their tendency to leam meaningfully, nor did th e students from the MVRL group alter their tendency to leam meaningfully. Perhaps if all classes in students’ schedules were tau g h t in th e same m anner, students’ learning orientations would change. Based upon my knowledge of my colleagues’ courses, th is was probably the only course in th e students’ week th a t did not reward rote learning. A concerted effort of aU professors might correlate w ith a positive change in meaningful learning orientation. Such a curriculum study should be done a t the college level. Theoretically, according to Piaget and Ausubel, great strides in meaningful understanding m ay be accomplished by students actively taking p a rt in th eir learning. Such understanding should greatly outweigh th a t obtained by hearing lectures. This research has already shown 81

th a t greater understanding occurred after each treatm ent. Theoretically, even greater understanding could occur if students’ tendency to leam meaningfully increased. Â study comparing th e change in meaningful learning orientation for th e LC and MVRL treatm ents to th a t of a traditional lecture/lab class should be conducted. Dickie (1994) found th a t students’ tendency to leam by rote

increased after a college physics class. Perhaps the students from the treatm ents in this study left the courses with a greater tendency to leam meaningfully than if they h ad been in a course th a t was taught traditionally by lecture/lab. Discussion of Question 2. Each student was assessed for each concept (forces, density/Archimedes’ Principle, and heat) on three submeasures of meaningful understanding: conceptual understanding, problem solving, and mental models. Results of ANCOVA’s revealed th a t there were no significant differences between the LC and MVRL treatm ents for students’ concept understanding (p > .149) of forces, densify/Archimedes’ Principle, and heat. The ANCOVA results for understanding measured by mental models also showed th a t there were no m easurable significant differences in meaningful understanding as measured by m ental models ip > .092). Thus, the students in the LC and MVRL treatm ents had roughly equal conceptual and m ental model understanding on all th ree items. Students fiom each treatm ent were encouraged to improve their conceptual knowledge and m ental model understanding. These findings provided more evidence for the idea fhat Piagetian and Ausubelian theories are similar theoretically if their endproducts (students’ conceptual understanding and mental model knowledge) are not significantly different.

According to results of ANCOVA’s, there were no statistically 82

significant difierences among treatm ents on the problem solving for forces. According to results of ANCOVA’s for densily/Archimedes’ Principle and heat data, th e problem solving differed in direction among ihe two treatm ents. For densiiy/Archimedes’ Principle data, the LC students had a 25% improvement in problem solving over the MVRL students’ mean scores (pc.006). For heat data, th e MVRL students had a 16% improvement in problem solving over the LC students (p< .019). This m ay simply indicate weaknesses in curricula for the two treatm ents. For forces, th e curricula appears to be equal for both treatm ents. For density/Archimedes’ Principle, the LC exploration was a problem solving activity similar to the problems on ihe assessm ent in stru m e n t The LC students actually measured ihe m ass of ih e w ater th a t poured out of ihe cup when a cylinder was put in ihe cup of w ater. They determined th a t th is quantity was th e same mass as ihe apparent m ass difference (buoyant force) of ihe cylinder in and out of water. T hat particular LC activity was an ideal opportunity to watch the students construct their ideas about densiiy/Archimedes’ Principle. The weakness of ihe MVRL curricula for densiiy/Archimedes’ Principle could be explained in Ausubelian term s. The verbal instruction on densiiy/Archimedes’ Principle did not to provide suitable anchors to other structures, thus creating less problem solving abiliiy by its students. A Piagetian explanation for the MVRL curricular weakness for ihe densiiy/Archimedes’ Principle topic m ight be th at there was no assimilation because of a lack of previous e3q>erience. I have noticed m any tim es over ihe years th a t students are unaware th a t ihe volume of w ater th a t comes out of a cup when a c>dinder is inserted, is ihe same as ihe volume of ihe qdinder. A lack of experience could possibly have caused ihe MVRL students to lag behind in densiiy/Archimedes’Principle problem solving. The heat problem solving difference may indicate a weakness in the 83

LC curriculum and a strength for the MVRL curriculum . From day one in th e MVRL treatm ent, stu d en ts were relating concepts to energy and heat. These students sim ply m ay have thought about h eat more and made more connections which increased their problem solving abiliiy. Perhaps students already had concrete experience with heat. T he LC curriculum did n o t stress heat from the beginning of the semester. The LC curriculum of th is study was modeled after one used in local school system s since 1986. Now, it is thought th a t LC curriculum m ust be planned so th a t "the concepts learned in earlier learning cycles can serve as anchors for linking concepts of later learning cycles” (M arek and Cavallo, 1997). This m eans th a t more general topics such as h eat and energy m ust be introduced first before specific item s such as motion and speed. The LC students did not have an earlier LC to provide anchors about heat, whereas the density LC prior to the Archimedes’ Principle LC did provide anchors. Thus, the LC students had less experience with heat according to Piaget or less prior knowledge about heat according to Ausubel. W hether explained in Piagetian term s (no assimilation occurred) or in Ausubelian term s (no subsumers were available), the LC students solved fewer problems on th e h eat concept th an the MVRL students did. Why the sam e differences between trea tm en t due to treatm ent weakness or strength did not appear on the conceptual and mental model assessments are unknow n. Possibly because th e m ental model and conceptual questions had a greater number of maximum points, th ere was more room for students’ meaningful understanding scores to fluctuate without being significantly different as a group. Note the problem solving scores had a possible score of six. The maximum possible conceptual scores were at least seventeen, and the mental model scores were much greater. Perhaps increasing th e point value for problem solving, allowing for partial credit might prove fimitfül in a similar füture investigation. 84

Conclusions from Question 2 According to the results of Question 1, Ausubelian and Piagetian theories used different term s to explain the construction of meaningful understanding. Also, manners of achieving meaningful understanding have been based upon each theory. Vl^th well-planned and well-written curricula and assessment instrum ents having the same maximum point-value, no differences should be expected between LC and MVRL treatm ents ff indeed th e two theories sim ply use different terminol(%y to explain meaningful learning. Discussion of Question 3. Based upon r^ re s s io n analyses, neither treatm ent, nor reasoning ability, nor meaningful learning orientation, nor prior knowledge were significant predictors of overall physics (concept + problem solving + m ental model) understanding a t the .05 level. For forces and density/Archimedes’ Principle, the students’ treatm ents were the best predictor, while for h e a t the students’ learning orientation scores were the best predictor. Thus for th e three concepts studied, none of the predictors were significant; and for th e three topics the m ost significant predictor of overall physics understanding was different. These findings further complicate our understanding of th e most important variable in meaningful understanding. I t may possibly m ean th a t all predictor variables are necessary or in some way interconnected. Or perhaps these instrum ents are not accurate m easures. As was m entioned in Chapter 2, past research has been contradictory on th is m atter as well. All variables m ust be examined in future research to determ ine what is m ost im portant to overall meaningful understanding of physics. Such research is critical for further understanding of meaningful learning and education in general.

85

Conclusions from Question 3. Veiy little m ay be concluded from the resu lts of Question 3 aside from the fact th a t more research must be conducted to determ ine what variables are the strongest predictors of overall physics understanding. Perhaps research w ith other instrum ents and well-tested curricula will yield more valuable results. The results of question 3 indicate and reinforce th a t meaningful understanding is complex. Discussion of Question 4. The results of a stepwise multiple regression to find the best predictor for forces, densify/Archimedes’Principle, and h ea t conceptual understanding proved more fruitful th an did the analyses for overall understanding. For forces and densify/Archimedes’Principle data, students’ prior knowledge was the best predictor of student conceptual understanding while reasoning abilify was the next best predictor. For heat, reasoning abilify was the only significant predictor of heat concept scores. W ithout prior experience, conceptual understanding decreased substantially for forces and for densify/Archimedes’ Principle. T hat is to be expected by both Piagetian and Ausubelian theories, for without assimilation or suhsumers, meaningful learning does n ot occur. According to Piaget w ithout adequate reasoning abilify, abstract concepts such as forces, densify/Archimedes’ principle, and heat can not be learned. Perhaps this is w hat Ausubel m eant when he used the term ^potentially meaningful’ as a criterion for meaningful learning. For Ausuhel, the evidence suggests th a t m aterial classified as not potentially meaningful would include material more abstract th an the studenffs structures. For problem solving understanding of force and heat concepts, reasoning abilify was th e best predictor. Thus, students having greater reasoning abilify correlated with greater problem solving. This can be 86

ejq)lained if Piagetian reasoning ability and Üie Ausubelian term "potentially meaningful" have sim ilar meaning. If forœs and h e a t were presented in a potentially meaningful way, then according to Ausubel meaningful learning measured by solving problems could occur. If forces and h eat were presented to formal operational learners, then according to P iaget th e construction of problem solving understanding could occur. For heat, th e next best predictor of problem solving was treatm ent, with MVRL treatm ent correlating with greater h e a t problem solving. For density/Archimedes’ Principle, the best predictor was treatm ent, with the LC treatm ent correlating w ith greater density/Archimedes’ Principle problem solving. This finding is consistent with the findings and discussion of Question 2. This may be explained by the apparent w eakness of the MVRL treatm ent to present the density/Archimedes’ Principle concept combined with the strength of th e LC to present the densify/Archimedes’ Principle concept and the app aren t strength of the MVRL presentation of heat combined with the apparent weakness of the LC presentation of h e a t In sh o rt the two curricula produced different levels of problem solving understanding for different concepts depending upon the relative strength of the curricula. None of the predictor variables (reasoning ability, prior knowledge, learning approach, or treatm ent) were significant predictors of the knowledge measured by m ental models. The inexperience of th e researcher with m ental models may be the cause of this finding. Mental models m ay be only valid as understanding m easures if the researcher has g reat deal of eiq)erience with them. Mental models should be examined fu rth er as tools to measure meaningful understanding of c o llie physics students. Conclusions from Question 4.

The analysis of predictor variables for concept understanding and 87

problem solving further support the idea th a t Piagetian and Ausubeiian theory are similar in th e ir explanation of how learning occurs. All variables mentioned in theories by Piaget and Ausubel were not significant predictors for concept understanding or problem solving, so exact correlations of the theories are not yet possible based on the findings of th is research. Question 4 analyses should be repeated w ith a LC curricula based on a top down approach, the MVRL phases sequenced in th e most beneficial order, and more reliable instrum ents. Once these corrections are made more insight will be gained into these two theories of learning. In summary according to this research, there w ere no significant differences between th e Piagetian-based learning cycle and th e Ausubelianbased meaningful verbal reception learning for college students’ meaningful understanding of physics concepts. W hat the results of this research suggested is th a t although Piaget and Ausubel used different terminology to explain learning, these theories are very similar. T his research attem pted to blend the two theories; illustrating th a t the theories did not explain meaningful understanding in significantly different ways. In doing so, there were far more questions raised th an have been answered. For example, where is the disequilibrium in Ausubel’s theory? W hat is the motivating factor in Ausubel’s theory th a t compares to the disequilibrium in Piaget’s theory? Is the learning orientation sufficient to m otivate the learner to make the necessary connections? If it is, w hat is the m otivating force for organization in Piagetian theory? F urther research is necessary to obtain answers to these questions.

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National Science Teachers Association (1993). Scope, sequence, and coordination of secondary school science: vnhimfi 1 the content core. Washington, D.C. Novak, J.D. (1984). Application of advances in learning theory and philosophy of science to the improvement of chem istry teaching. Journal of Chemical Education. 61(7). 607-612. Novak, J.D. (1988a). Learning science and the science of learning. Studies in Science Education. 15. 77-101. Novak, J.D. (1988b). Assessing student learning in hght of how students leam . Paper collected as p art of the American Association for Higher Education Reform, American Association for H igher Education: Washington, D.C. Novak, J.D. (1993). Momningful learning: the essential factor for conceptual changR in limited or inappropriate positional hierarchies (LIPH’s) leading to empowerment for learners. Paper presented a t the opening lecture of the TTiird International Seminar on Misconceptions and Edu­ cational Strategies in Science and Mathematics, Ithaca, NY, August 1, 1993. Novak, J.D., & (jowin, D.B. (1984). Learning how to leam . Cambridge: Cambridge University Press. Novak, J.D., Gowin, D.B., & Johansen, G.T. (1983). The use of concept mapping and knowledge Vee mapping with junior high school science students. Science Education, 67(5), 625-645. Novak, J.D., & Musonda, D. (1991). A twelve-year longitudinal study of science concept learning. Ameriran Educational Research Journal, m i ) , 117-153.

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Okebukola, P A . (1990). A ttaining meaningful learning of concepts in genetics and ecology: an examination of the potency of the concept-mapping technique. Journal of Research in Science Teaching. 27(51 493-504. Piaget, J. (1963). The origins of intelligence in children. New York: Norton. Piaget, J. (1970). Science of education and the psychology of the child. (D. Coltman, Trans.). New York: Orion. (Original work published 1969). Pines, A L ., & Novak, J.D. (1985). The interaction of audio-tutorial instruction with student prior knowledge: a proposed qualitative, case-study methodology. Science Education. 69(2). 213-228. Pines, A L ., & West, L.H.T. (1986). Conceptual understanding and science learning: an interpretation of research w ithin a sources of knowledge framework. Science Education. 70(5). 583-604. Prosser, M. (1983). Relationship between the cognitive abilities of a group of tertiary physics students and th e cognitive requirements of their textbook. Science Education. 67(1). 75-83. Purdom, D.M., & Kromrey, J.D. (1992). A comparison of different instructor intervention strategies in cooperative learning groups a t the college level. Paper presented a t the Annual Meeting of the American Educational Research Association, San Francisco, CA, April 20-24,1992. Purser, R.K., & Renner, J.W. (1983). Results of two tenth-grade biology teaching procedures. Science Education. 67(1). 85-98. Ramsden, P., & Entwistle, N.J. (1981). Effects of academic departm ents on students’ approaches to studying. British Journal of Educational Psvcholopv. 51(3). 368-383.

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Renner, J.W. (1986). Curricula which promote uprfprstenHing. Paper presented a t the U.S.-Japan Seminar on Science Education, Honolulu, HI, Sept. 14-20, 1986. Renner, J.W., Abraham, M.R., Grzybowski, E.B., & Marek, E.A. (1990). Understandings and misunderstandings of eighth graders in four physics concepts found in textbooks. Journal of Research in Science Teaching. 27(1). 35-54. Renner, J.W., & Marek, EA . (1988). The learning cvcle and elem entary school science teaching Portsmouth, NH: Heinemann. Renner, J.W., & Marek, E.A. (1990). An educational theory base for science teaching. Journal of Research in Science Teaching. 27(3). 241-246. Renner, J.W., & Paske, W.C. (1977). Comparing two forms of instruction in college physics. Ampripan Journal of Phvsics, 45(9). 851-859. Renner, J.W., Stafford, D.G., Lawson, A.E., McKinnon, J.W., Friot, F.E., Kellogg, D.H. (1976). Research, teaching, and learning with the Piaget model. Norman, OK: University of Oklahoma Press. Resnick, L. B., & Ford, W. W. (1981). The psychology of m athem atics for instruction. Hillsdale, NJ: Lawrence Erlbaum Associates. Rubin, A., & Tamir, P. (1988). Meaningful learning in the school laboratory. The American Biology Teacher. 50(8). 477-482. Saunders, W., & Shepardson, D. (1984). A comparison of concrete and formal science instruction upon science achievement and reasoning ability of sixth grade students. Paper presented at Annual Meeting o f the National Assoc, for Research in Science Teaching, New Orleans, LA, April 28, 1984. Schneider, L.S., & Renner, J.W. (1980). Concrete and formal teaching. Journal of Research in Science Teaching. 17(6). 503-517. Schwebel, M (1975). Formal operations in first-year college students. Journal of Psychology. 91. 133-141. 96

Shayer, M., & Adey, P.S. (1992). Accelerating th e development of formal thinking in middle and high school students EQ; testing the perman­ ency of effects. Journal of Research in Science Teaching. 29(101 1101-1115. Stepans, J., Dyche, S., & Beiswenger, R. (1988). The effect of two instructional models in bringing about a conceptual change in the under­ standing of science concepts by prospective elem entary teachers. Science Education. 72(2). 185-195. Sunal, D. & others. (1992). Forest, land, and water: unHermtanding our natural resources-natural resources education series. Washington, DC: Forest Service (DOA) Taylor, M R. (1985). Changing the m eaning of experience: empowering learners through the use of concept mans. Vee diagrams, and principles of educating in a biology lab course [CD-ROM]. Abstract from: ProQuest File: D issertation Abstracts Item: 8516993 Trifone, J. D. (1991). Addressing the needs of the concrete reasoner. American Biologv Teacher. 53(6). 330-333. Tobin, K G ., & Capie, W. (1981). The development and validation of a group te st of logical thinking. Educational and Psychological Measurement. 41(2), 413-423. Trowbridge, J.E., & Wandersee, J.H. (1994). Identifying critical junctures in learning in a college course on evolution. Journal of Research in Science Teaching. 31(5). 459-473. Wadsworth, B.J. (1989). Piaget's theory of cognitive and affective development. New York: Longman. Wandersee, J.H . (1988). Ways students read texts. Journal of Research in Science Teaching. 25(1). 69-84. Weems, B. (1990). General phvsics 1114/1214 laboratory manual. Edina, MN: Alpha Editions. 97

Westbrook, S.L., & Marek, E.A. (1991). A cross-age study of student understanding of the concept of diffusion. Journal of Research in Science Teaching. 2^(8), 649-660. Westbrook, S.L., & Marek, E.A (1992). A cross-age study of student understanding of the concept of homeostasis. Journal of Research in Science Teaching, 29(1), 51-61. Westbrook, S.L., & Rogers, L.N. (1991). An analysis of the relationship between student-invented hypotheses and the development of reflective thinking strategies. Paper presented a t the Annual Meeting of the National Association for Research in Science Teaching, Lake Geneva, WI, April 7-10, 1991. Williams, K. (1997). Densitv/Archimedes* principle-a study and demonstration. Paper presented at the Fall Meeting of the ArkansasOklahoma-Kansas Section of the American Association of Physics Teachers, M anhattan, KS, Oct. 25, 1997. Williams, K.A, & Cavallo, AM. (1994). One more reason to teach so th a t students don’t ju st memorize. Paper presented a t the American Association of Physics Teachers Summer Meeting, Notre Dame, IN, Aug. 10, 1994. Williams, K.A., & Cavallo, AM. (1995). Relationships between reasoning ability, meaningful learning and students’ understanding of physics concepts. Journal of CoUege Science Teaching. 24(5). 311-314.

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APPENDICES Appendix A- Student Permission Letter Appendix B- Instrum ents Test of Logical Thinking (TOLT) Learning Approach Questionnaire (LAQ) Forces: Conceptual Questions Forces: Problems Forces: M ental Model Density/Archimedes’ Principle: Conceptual Questions Density/Archimedes’ Principle: Problems Density/Archimedes’ Principle: M ental Model Heat: Conceptual Questions Heat: Problems Heat: Mental Model Mental Model Template Appendix C- Learning Cycles Graphing Laws of Motion Motion of Ball on Incline Motion of Ball on Steeper Incline Motion of Falling Ball Vectors Friction Circular Motion Energy The Balancing Act Collisions and th e Rules th a t Govern Them Density Archimedes’Principle Specific H eat in Solids Appendix D- Meaningful Reception Learning Concept Maps Figure 1: Energy Figure 2: Energy and M atter Figure 3: Therm al Expansion, H eat and Thermometers Figure 4: S tudent Map on Heat Figure 5: S tu d en t Map on Heat Figure 6: Newton’s Laws Figure 7 and 8: Energy Methods Figure 9: Energy, M atter, Energy, Density Figure 10: Student Map on M atter Figure 11: Student Map on Energy, M atter, Density, Pressure Figure 12: Archimedes’ Principle Figure 13: Falling Objects Appendix E- Miscellaneous Statistics Table 10: ANCOVA Adjusted Means Tables 11-13: Pearson Correlation Matrices Tables 14-16: Descriptive Statistics

99

APPENDIX A: Student Permission Letter

100

_ Tfie iM versi^ ( f OftCafioma •OMM mcAnoN camn

W H ilH l a c t— » Wanm 323 N o n i m O k W o n a 7301»

Agreement to participate This letter is to obtain your consent to participate in a research project by Karen Williams, Asst. Professor at ECU & PhD student at OU, under the sponsorship of Dr. Ed Marek a professor of science education a t OU (OU, Science Education (Center, Physical Sciences Bldg, Rm 323, Norman, OK 73019, phone 405/325-1498). The research is to be conducted a t ECU, but under the auspices of the University of Oklahoma-Norman Campus. Please read all of this agreement carefully and sign if you agree to participate. Because both sections of GPI t a u ^ t this semester are given specialized treatm ent Üiis semester, if you do not agree to participate in the course format as is taught, you must drop this course and enroll again at a later time without any prejudice against you. If you want to participate in the course as taught, but without your scores being used, you may remain enrolled in the course without prejudice to you and I will not use your scores in the study. The purpose of this research is to determine the effects that a learning cycle style physics class and a meaningful verbal reception style physics class have upon your understanding of physics concepts and your approach to learning. Learning qycles are labs designed to allow concept learning. In reception learning, the teacher provides an outline of material to which s/he later attaches more specific material. Then students organize this material into diagrams of how the material is related. The participants of (he study will be asked before and after instruction to complete, multiple choice exams, work 6 problems, and tell all s/he knows about particular physics concepts (i.e. forces). As with any physics exam that assesses knowledge, these exams will count in the calculation of your grade as described in the sjdlabus. Such exams have been given in "ordinary physics courses” previously taught by the instructor that were not involved in any study. In addition to the physics tests, the participants reasoning ability and approach to learning will be assessed primarily th ro u ^ multiple choice exams. These two exams will not affect your grade. I sign this (______________________ 1as evidence that I do not foresee any mental or physical risks to any of the participants of this study that do not also exist in any normsd physics course taught at ECU by K. Williams. On the other hand, participants in both classes may benefit by greater physics understanding as well as having gained a vigorous approach to learning th at will be invaluable throughout your education. Neither I nor past research can tell you which class (if one is really better Üian the other) will provide the best understanding. Thus there is no known disadvantage or advantage at this time to being in one section as opposed to the other. This is to certify that I , ____________________________, hereby agree to participate as a (print full name) volunteer in a scientific investigation as a p art of an authorized research program of the University of Oklahoma Science Education Center. I understand that this allows my scores to be used in research, but th at my name will not be used in association with such scores reported in research. I understand and was told that I am free to refuse to participate in any part of this project without prejudice or detriment to me. I understand th at by signing this form, I agree to participate in this research. However, this does not waive my legal rights. I understand th at the OU Science Eld. (Center or K. Williams will answer any questions I have relating to the research procedures. Date

Subject’s signature

101

APPENDIX B: Instrum ents Test of Logical Thinking (TOLT) Learning Approach Questionnaire (LAQ) Forces: Conceptual Questions Forces: Problems Forces: Mental Model Density/Archimedes’ Principle: Conceptual Questions Densiiy/Archimedes’ Principle: Problems Density/Archimedes’ Principle: Mental Model H ea t Conceptual Questions Heat: Problems Heat: Mental Model Mental Model Template

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T est o f L ogical T h in k in g (TOLT) WRITE ONLY ON THE ANSW ER SH EET PROVIDED. Item 1: Orange Juice I.

Four oranges are squeezed to make six glasses of juice. How much juice can be made from six oranges? A. B. C. D. E.

n.

7 glasses 8 glasses 9 glasses 10 glasses other

Reason A. B. C. D. E.

The num ber of glasses compared to th e num ber of oranges will always be in the ratio of 3 to 2. With more oranges, the difference will be less. The difference in the numbers will always be two. With four oranges the difference was 2. W ith six oranges the difference would be two more. There is no way of predicting. Item 2: Orange Juice

I. Given the information in Item 1, how m any oranges are needed t o make 13 glasses of juice? A. B. C. D. E. n.

6 1/2 oranges 8 2/3 oranges 9 oranges 11 oranges other

Reason A. B. C. D. E.

The num ber of oranges compared to the num ber of glasses will always be in the ratio 2 to 3. If there are seven more glasses, th en five more oranges are needed. The difference in the numbers will always be two. The num ber of oranges will be h alf th e num ber of glasses. There is no way of predicting the num ber of oranges.

103

Item 3: The Vegetable Seeds I. A gardener bought a package containing 3 squash seeds and 3 bean seeds. I f ju s t one seed is selected from th e package w hat are the chances tiia t it is a bean seed? A. B. C. D. E.

n.

1 out of 2 1 out of 3 1 out of 4 1 out of 6 4 out of 6

R eason A. B. C. D. E.

Four selections are needed because the three squash seeds could have been chosen in a row. T here are six seeds finm w hich one hean seed m ust be chosen. One bean seed needs to be selected from a total of three. One h alf of the seeds are bean seeds. In addition to a bean seed, th ree squash seeds could be selected from a total of six.

Ite m 4: The Flow er Seeds I.

A gardener bought a package of 21 mixed flower seeds. The package contained seeds for: 3 sh o rt red flowers 4 sh o rt yellow flowers 5 sh o rt orange flowers

4 tall red flowers 2 tall yellow flowers 3 ta ll orange flowers

If ju s t one seed is planted, w hat are th e chances th a t the plant th a t grows will have red flowers? A. D.

n.

1 out of 2 1 out of 21

B. E.

2 out of 3 other

C.

1 out of 7

R eason A. B. C. D. E.

One seed has to he chosen from am ong those th a t grow red, yellow, or orange flowers. 1/4 of fhe shortand 4/9 of th e ta ll are red. I t does not m atter w hether a ta ll or a short is picked. One red seed needs to be picked from a to tal of seven red seeds. One red seed m ust be selected from a total of 21 seeds. Seven of the twenty-one seeds w ill produce red flowers.

104

U se the diagram below to help you answ er Item s 5 and 6. The diagram shows five pendulum s of various lengths. The num ber a t th e bottom of each pendulum is th e num ber of large steel w ashers (W) attached to th e end of the pendulum. 1

2

3

4

5

4W

low

5W 5W 3W

Ite m 5: The Pendulum 's Length I. Suppose you w anted to do an experim ent to find out if changing th e length of a pendulum changed th e am ount of tim e it takes to swing back and fortii. W hich pendulum s would you use for th e experiment? A. 1 and 4

n.

B. 2 and 4

C. 1 and 3

D. 2 and 5

E. all

Reason A. B. C. D. E.

The longest pendulum should be tested against the sho rtest pendulum. All pendulum s need to be tested against one another. As d ie length is increased th e num ber of w ashers should be decreased. The pendulum s should be th e sam e length b u t the num ber of w ashers should be different. The pendulum s should be different lengths bu t the num ber of w ashers should be th e same.

105

Item 6: The Pendulum's Weight I. Suppose you w anted to do an experim ent to find out if changing the weight on th e end of th e string changed th e am ount of th e tim e th e pendulum takes to swing back and forth. Which pendulum s would you use for the experiment? (refer to previous diagram) A. 1 and 4 n.

B. 2 and 4

C. 1 and 3

D. 2 and 5

E. all

Reason A. B. C. D. E.

The heaviest w eight should be compared to th e ligh test w eight All pendulum s need to be tested against one another. As Üie num ber of washers is increased th e pendulum should be shortened. The num ber of w ashers should he different b u t th e pendulum s should be th e same length. The num ber of w ashers should be the sam e b u t th e pendulum s should be different lengths.

106

Item 7: The Mice

I. The mice show n above represent a sam ple of m ice captured from a p art of a field. A re large mice more likely to have black tales and sm all mice more likely to have w hite tails? A. n.

Yes

B.

No

Reason A. B. C. D. E.

8/11 of th e large mice have black tails and 3/4 of th e sm all mice have w hite tails. Some of the large mice have w hite tails and some of th e sm all mice have w hite tails. 18 mice out of 30 have black tails and 12 have w hite tails. N ot all of & e large mice have black tails and not all of the sm all mice have w hite tads. 6/12 of th e w hite taded mice are large.

107

Item 8: The Fish

L The fish show n above represent a sam ple of fish captured fi*om a p a rt of a lake. Are large fish m ore likely to have broad stripes than sm all fish? Yes n.

B,

No

Reason A. B. C. D. E.

Some larg e fish have broad stripes and some have narrow stripes. 1/4 of th e fish are large 12/28 are broad striped and 16/28 are narrow striped. 3/7 of th e large fish have broad stripes and 9/21 of the sm all fish have broad stripes. Some fish w ith broad stripes are sm all and some are large.

108

Item 9: The Student Council Three students from each of grades 10,11, and 12 were elected to the student council. A th ree member committee is to be form ed with one person from each grade. All possible combinations m ust be considered before a decision can be made. Two possible com binations are Tom, Jerry, an d D an (TJD), and Sally, Anne, and M artha (SAM). L ist all other possible combinations in th e spaces provided on your answ er sheet. More spaces are provided than you will need. Grade 10

G rade 11

Grade 12

Tom (T)

Je rry (J)

Dan (D)

Sally (S)

Anne (A)

M artha (M)

Bill(B)

Connie (C)

Gwen(G)

Ite m 10: The Shopping Center In a new shopping center, 4 store locations are going to be opened on th e ground level. A BARBER SHOP (B), a DISCOUNT STORE (D), a GROCERY STORE (G), and a COFFEE SHOP (C) w ant to move in there. Each one of th e stores can choose any one of four locations. One w ay th a t th e stores could occupy th e four locations is BDGC. L ist all other possible ways th a t the four stores can occupy the 4 locations in th e spaces provided on your answ er sh e et More spaces are provided th an you will need.

109

L earn in g A pproach Q u estion n aire (LAQ) Learning in Science and in School (L earning Approach Q uestionnaire)

W rite your nam e, your b irth date, and your sex on th e scantron provided. The questions in this booklet are about how you study and leam Respond to every question by com pletely filling in the letter you choose on th e scantron provided. P lease use a #2 pencil. Do not m ark in th is booklet. Work quickly through th e questions, your first answ er is usually your best. There are no rig h t or wrong answers. Simply respond according to how you think and feel. Please be assured th a t your answ ers are confidential.

T hank you very m uch for your cooperation in answ ering th e questions.

110

1. Age: a. 15-19

b. 20-24

c. 25-29

2. E thnic O rigm :

a. Am erican In d ian c.W bite/C aucasian e. other

d. 30-39

e. 40+

b. A sian d.Afirican/American

3. M other's H ighest Level of Education Completed: a. less th a n high school b. high school graduate c. som e college d. college graduate e. beyond c o llie (graduate w ork, m edical school, law school, etc.) 4. F ath er's H ip e s t Level of Education Com pleted: a. less th a n high school b. high school graduate c. som e college d. college graduate e. beyond college (graduate w ork, m edical school, law school, etc.) 5. W hat is yo ur classification so far? a. F r b. So. c. J r.

d. Sr.

e. G rad.

6. W hat is you r grade in th is physics class? a. A b. B c. C

d. D

e. F

7. W hat grade would you give yourself on your reading ability? a. A b. B c. C d. D e. F 8. W hat grade would you give yourself on your ability to express yourself in writing? a. A b. B c. C d. D e. F 9. Do you p la n to tak e an y more science courses after th is one? a. Yes, definitely b. yes, probably c. no, probably d. No, definitely e. I don't know

111

T he following questions refer to how you stu d y an d le a m ab ou t_______ in th is class. F or each item th ere is a five point scale r a n g in g fi*om "Always True" to "N ever True". On th e scantron provided, fill in th e letter th a t best fits your im m ediate reaction. Do not spend a long tim e on each item; your firs t reaction is probably th e best one. A nsw er every question. D on't w orry about projecting a good image. There are no correct answ ers and your answ ers are confidential! Always True— Never T rue A B O D E 10.

I generally p u t a lot of effort into try in g to understand things which a t firs t seem difScult.

0

0 0 0 0

11.

I have a fairly good grasp of the m ain ideas of a topic b ut my knowledge of th e details is ra th e r weak.

0

0 0 0 0

12.

I try to re la te new m aterial, as I am learning it, to w hat I already know on th a t topic.

0

0 0 0 0

13.

I prefer to follow all "tried out" w ays to solve problems rath er th a n try in g anything too adventurous.

0

0 0

0 0

14.

W hile I am studying, I often th in k of real life situations to which the m aterial I am learning would be useful.

0

0

00

15.

I find I ten d to rem em ber things b est if I concentrate on the order in w hich th e teacher presented them.

0

0 0 0 0

16.

I find I have to concentrate on m em orizing a good deal of w hat I have to leam .

0

0 0

0 0

17.

I go over im portant topics until I u n d erstan d them completely.

0

0 0

0 0

112

0

Always True— Never True A B O D E 18.

I find it best to accept the statem en ts and ideas of my lectures and question them only un d er special circum stances.

0 0

0 0 0

19.

I prefer courses to be tau g h t in a w ay th a t is clearly structured and h i^ y o rg a n iz e d .

0 0

0 0 0

20.

T eachers shouldn't expect students to spend significant am ounts of tim e studying m aterial everyone knows w on't be examined.

0 0

0 0 0

21.

In reporfing laboratory work, I like to try to w ork out several different w ays of interpreting the findings.

0 0

0 0 0

22.

I often find m yself questioning th ing s th a t I h ear in lectures or read in books.

0 0 0

23.

In try in g to understand new topics, I explain them to myself in ways th a t other people don't seem to u n d erstan d

0 0 0 0 0

24.

I find it useful to get an overview of a new topic for myself, by seeing how th e ideas fit together.

0 0 0 0 0

25.

Teachers seem to delight in m aking th e sim ple tru th unnecessarily com plicated.

0

26.

A fter a lecture or lab, I reread my notes to m ake sure th a t I understand them .

0 0 0 0 0

27.

I se t out to understand th o ro u ^ily th e m eaning of w hat I am asked to read or learn in class.

0 0 0 0 0

113

0 0

0 0 0 0

Always True— Never True A B C D E 28.

I ten d to like subjects w ith a lot of factual content ra th e r th a n theoretical kinds of subjects.

0

0 0

0 0

29.

I try to relate w hat I have learned in one subject to th a t in another.

0

0 0

0 0

30.

I feel th a t I am more cautious th a n others in draw ing conclusions, unless th ey are well supported by evidence.

0

0

0

0 0

31.

T he best w ay for me to understand w h at technical term s m ean is to rem em ber th e textbook definition.

0

0

0

0 0

32.

I am very aw are th a t teachers know a lot more th an I do, and so I concentrate on w hat they say as im p ortant ra th e r th an rely on m y own judgm ent.

0

0 0

0 0

33.

Puzzles and problems fascinate me, particularly where you have to w ork through the m aterial to reach a logical conclusion.

0 0

0

0 0

34.

I u su ally don't th in k about the im plications of w hat is tau gh t in class or how it relates to my life.

0 0

0

0 0

35.

I le a m some things by rote, going over and over them until I know them by h eart.

0 0 0

0 0

36.

W hen I'm startin g a new topic, I a sk m yself questions about it w hich th e new inform ation should answ er.

0 0

0

0 0

37.

I spend a lot of my free tim e finding o u t m ore about in teresting topics which have been discussed in class.

0

0 0

114

0

0

Always True— Never True A B O D E 38.

I often have to read things in physics w ithout really understanding them .

0 0 0 0 0

39.

A lthough I generally rem em ber facts and details, I find it difidcult to fit them together into an overall picture.

0

40.

W hen I am reading an article or listening to other's ideas in class, I generally exam ine th e evidence carefully to decide w hether th e conclusion is justified.

0 0 0 0 0

41.

I generally restric t my study to w hat is specifically set as I th in k it is unnecessary to do anything extra.

0 0

42.

W hat I have learned in this class h as changed my views about some things in life (for example: politics, religion, philosophy oflife)

0 0 0 0 0

115

0 0 0 0

0 0 0

F orces C oncep tu al Q u estion s P la ce th e le tte r o f th e correct an sw er on th e sca n tro n sh eet. 1. Two m etal balls are th e same SIZE, but one weights twice as much as the other. The balls are dropped from the top of a two story building at the same tim e. The time it takes the balls to reach th e ground below will be: a. b. c. d. e.

about h alf as long for the heavier ball. about h alf as long for the lighter ball. about the sam e tim e for boüi balls. considerably less for the heavier ball, but not necessarily half as long. considerably less for the l i f t e r ball, but not necessarily half as long.

2. Imagine a head-on collision between a large truck and a small compact car. During the collision, a. the truck exerts a greater amount of force on the car than the car exerts on the truck. b. the car exerts a g reater am ount of force on the truck than the truck exerts on the car. c. neither exerts a force on the other, the car gets smashed simply because it gets in the way of th e truck. d. the trudc exerts a force on the car, but the car doesn't exert a force on the truck. e. the truck exerts th e same amount of force on the car, as the car exerts on the truck. 3. Two steel balls, one of which weighs twice as much as the as the other, roll off a horizontal table w ith the same speeds. In this situation; a. both balls im pact the floor a t approximately the same horizontal distance from the base of th e table. b. the heavier ball im pacts the floor a t about half the horizontal distance frrom the base of the table t h a n does the lif t e r . c. the lighter ball im pacts the floor a t about half the horizontal distance from the base of die table t h a n does the heavier. d. the heavier ball h its considerably closer to the base of the table th an the lighter, but not necessarily h a l f the horizontal distance. e. the lighter ball h its considerably closer to the base of the table than the heavier, but not necessarily h alf the horizontal distance. 4. A heavy ball is attached to a string and swung in a circular path in a horizontal plane as illustrated in th e diagram on the right. At the point indicated in the diagram, the string suddenly breaks a t the ball. If these events were observed from directly above, indicate the path of the ball after the string breaks.

‘f (a,

(4 . 116

5. A boy throw s a steel ball s tr a i^ t up. Disregarding any eCTects of air resistance, the forcels) acting on the ball until it returns to the ground is(are): a. its w e i^ t vertically downward along with a steadily decreasing upward force. b. a steachly decreasing upward force firom the moment it leaves Üie hand until it reaches its hiid^est point beyond which there is a steadily increasing downward force of gravity as Üie object gets closer to the earth. c. a constant downward force of gravity along with an upward force th a t steadily decreases until the ball reaches its fa ire s t point, after which there is only the constant downward force of gravity. d. a constant downward force of gravity only. e. none of th e above, the ball falls back down to the earth simply because th a t is its n atu ral action. Use th e statem ent and diagram below to answer the next four questions: The diagram depicts a hockey puck sliding, with constant velocity, from point "a" to point "b” along a frictionless horizontal surface. When the puck reaches point "b", it receives an instantaneous horizontal Tdck" in the direction of the heavy p rin t arrow. a ~

b ~

— ————

— — — —— — —

6. Along which of the paths will the hockey puck move after receiving the Tdck"?

^

i

7. The speed of the puck ju st after it receives the Tdck"? a. b. c. d. e.

E qual to th e speed "Vo" it had before it received the Tdck". E qual to the speed "V" it acquires from the Tdck”, and independent of the speed "Vo". E qual to th e arithm etic sum of the speeds "Vo" and "V". Sm aller th an either of speeds "Vo" or "V". G reater th a n either of the speeds "Vo" or "V", but sm aller t h a n the arithm etic sum of these two speeds.

8. Along th e frictionless path you have chosen, how does the speed of the puck vary after receiving the Tdck"? a. No change. b. Continuously increasing. c. Continuously decreasing. d. Increasing for a while, and decreasing thereafter. e. D ecreasing for a while, and increasing thereafter.

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9. H ie main forces acting, after the Idck”, on the puck along the path you have chosen are: a. the downward force due to gravity and the effect of air pressure. b. the downward force of gravity and the horizontal force of momentum in the direction of motion. c. the downward force of gravity, the upward force exerted hy the table, and a horizontal force acting on the puck in the direction of motion. d. the downward force of gravity and an upward force exerted on the puck by th e table. e. gravity does not exert a force on the puck, it falls because of the intrinsic tendency of the object to fall to its natu ral place. 10. The accompanying diagram depicts a semicircular channel th at has been securely attached, in a horizontal plane, to a table top. A ball enters the channel at ”1" and exits at "2". Which of the p ath representations would most nearly correspond to the path of the ball as it exits the channel at "2" and rolls across the table top?

(4 M

11. Two students, a student "a" who has a m ass of 95 kg and a student t " who h as a mass of 77 kg sit in identical ofGce chairs facing each other. Student "a" places his bare feet on student "b'"s knees, as shown below. Student "a* then suddenly pushes outw ard with his feet, causing both chairs to move. In this situation.

a'

a. b. c. d. e.

neither student exerts a force on the other. student "a" exerts a force on "b", but "b" doesn't exert any force on "a". each student exert a force on the other b u t t " exerts the larger force. each student exert a force on the other bu t "a" exerts the larger force. each student exerts the sam e force on the other.

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12. A book is a t rest on a table top. Which of the following force(s) is(are) acting on the book? 1. A downward force due to gravity. 2. The upw ard force by the table. 3. A net downward force due to air pressure. 4. A net upw ard force due to air pressure. a. I only b. 1 and 2 c. 1,2, and 3 d. 1,2, and 4 e. none of these, since the book is a t rest there are no forces acting on it. Refer to the following statem ent and diagram while answering the next two questions. A large truck breaks down out on the road and receives a push back into town by a small compact car.

k

0= 0=013. While the car, still pushing on the truck, is speeding up to get up to cruising speed, a. the am ount of force of the car pushing against the truck is equal to th at of the truck pushing back against the car. b. the am ount of force of the car pushing against the truck is less than th a t of the truck pushing back against the car. c. the am ount of force of the car pushing against the truck is greater th a n th a t of the truck pushing back against the car. d. the car's engine is running so it applies a force as it pushes against the truck, b u t the truck's engine is not running so it can't push back against the car, the truck is pushed simply because it is in the way of the car. e. neither the car nor the truck exert any force on the other, the truck is pushed forward simply because it is in the way of the car. 14. After the person in the car, while pushing th e truck, reaches cruising speed at which he/she wishes to continue to travel a t constant speed; a. the am ount of force of the car pushing against the truck is equal to th at of the truck pushing back against the car. b. the am ount of force of th e car pushing against the truck is less than th at of the truck pushing back against the car. c. the amount of force of the car pushing against the truck is greater than th a t of the truck pushing back against the car. d. the car's engine is running so it applies a force as it pushes against the truck, but the truck's engine is not running so it can't push back against the car, the truck is pudied simply because it is in the way of the car. e. neither the car nor the truck exert any force on the other, the trudc is pushed forward simply because it is in the way of th e car. 15. When a rubber ball dropped fiom rest bounces off the floor, its direction of motion is reversed because; a. b. c. d. e.

energy of the ball is conserved. momentum of the ball is conserved. the floor exerts a force on the ball th at stops its fall and then drives it upward. the floor is in the way and th e ball has to keep moving. none of the above.

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16. Which of the paths in the diagram to the right best represents the path of the cannon ball?

17. A stone falling from the roof of a single story building to the surface of the earth; a. reaches its maximum speed quite soon after release and then falls at constant speed thereafter. b. speeds up as it falls, prim arily because the closer the stone get to the earth, the stronger the gravitational attraction. c. speeds up because of the constant gravitational force acting on it. d. falls because of the intrinsic tendency of all objects to fall toward the earth. e. falls because of a combination of the force of gravity and the air pressure pushing it downward. W hen responding to the following question, assume th at any frictional force due to air resistance are so small th a t they can be ignored. 18. An elevator, as illustrated, is being lifted up an elevator shaft by a steel cable. W hen the elevator is moving up the shaft a t constant velocity;

steel cable

ascending at constant speed a. the upward force on the elevator by the cable is greater than the downward force of gravity. b. the amount of upw ard force on the elevator by the cable is equal to th at of the downward force of gravity. c. the upward force on the elevator by the cable is less than the downward force of gravity. d. it goes up because th e cable is being shortened, not because of the force being exerted on the elevator by the cable. e. the upward force on the elevator by the cable is greater than the downward force due to Üie combined effects of air pressure and the force of gravity.

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19. Two people, a large m an and a boy, are pulling as hard as they can on two ropes attached to a crate as illustrated in the diagram on the right. Which of the indicated path (A-E) would most likely correspond to the path of the crate as they pull it along? man

boy

20. A golf ball driven down a fairway is observed to travel through the air with a trajectory (flight path) sim ilar to th a t in the depiction below. Which of the following force(s) is(are) acting on the golfball during its entire flight?

1. the force of gravity

2. the force of the "hit"

a. 1 only

c. 1,2, and 3

b. 1 and 2

d. 1 and 3

3. the force of air resistance e. 2 and 3

21. A bowling ball accidentally falls out of the cargo bay of an airliner as it flies along in a horizontal direction. As seen fiom the ground, which path would the bowling ball most closely follow after leaving the airplane?

A B When answering the next four questions, refer to the following statem ent and diagram. A rocket, drifting sideways in outer space from position "a" to position "b" is subject to no outside forces. At "b”, the rocket's engine starts to produce a constant thrust a t right angles to the line "ab". The engine turns off again as the rocket reaches some point "c". a

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22. Which p ath below best represents the path of the rocket between "b" and”c"?

b B 23. As the rocket moves from t " to "c", its speed is a. b. c. d. e.

constant. continuously increasing. continuously decreasing. increasing for a while and constant thereafter. constant for a while and decreasing thereafter.

24. At "c" the rocket's engine is turned off. Which of the paths below will the rocket follow beyond ”c"?

Î 0 B

c

C

0 E

25. Beyond ”c", the speed of the rocket is ; a. b. c. d. e.

constant. continuously increasing. continuously decreasing. increasing for a while and constant thereafter. constant for a while and decreasing thereafter.

26. A large box is being pushed across the floor a t a constant speed of 4.0 m/s. W hat can you conclude about the forces acting on the box? a. If the force applied to the box is doubled, the constant speed of the box will increase to 8.0 m/s. h. The am ount of force applied to move the box a t a constant speed m ust be more than its weight. c. The amount of force applied to move the box a t a constant speed m ust be equal to the am ount of the frictional force th at resists its motion. d. The am ount of force applied to move the box a t a constant speed m ust be more to the am ount of the frictional force th at resists its motion. e. There is a force being applied to the box to make it move h u t the external forces such as friction are not "real” forces they ju st resist motion.

122

27. I f the force being applied to the box in the preceding problem is suddenly discontinued, the box wül; a. b. c. d. e.

stop immediately. continue a t a constant speed for a very short period of time and then slow to a stop. immediately start slowing to stop. continue a constant velocity. increase its speed for a very short period of tim e, then start slowing to a stop.

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F orces: P rob lem s. S h o w a ll w ork. N am e:______________S tu d en t #:

C lass L ectu re tim e:

1. Two perpendicular forces, one of 45 N directed due N orth and th e second, 60 N dh-ected due E ast, act sim ultaneously on an object w ith m ass of 35 kg. W hat is th e resu ltan t acceleration of the object? 2. A block having a m ass of 5.0 kg re sts on a horizontal surface where th e coefficient of sliding kinetic M ction betw een th e two is 0.2. A string attached to th e block, is pulled horizontally resulting in a 2 m/sec^ acceleration by th e block. W hat is th e tension in th e string? 3. A 15 kg block and a 5.0 kg hanging m ass are connected by a light strin g over a m assless frictionless pulley. W hat is th e acceleration of th e system when released? 4. A horizontal force of 750 N is needed to overcome th e force of static friction betw een a level floor and a 250 kg crate. W hat is th e coefficient of static fiiction? 5. A 300 kg crate is placed on an a4justahle inclined plane. As one end of th e incline is raised, the crate begins to move downward ju s t as the angle of inclination reaches 25 d ^ re e s . W hat is th e coefficient of static friction betw een th e crate and incline surface? 6. A puck is given an initial speed o f 8 m/sec after being h it by a hockey stick. I t continues to move in a straig h t line path for a distance of 16 m before coming to rest. W hat is th e negative rate of acceleration? W hat is th e force on the puck? (m ass of puck= 1(X). g)

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F orces: M ental M odel Name:___________ Student#:______Class Lecture Time:____ W rite everything th a t you know about forces. Include anything th a t may help illu strate your knowledge of forces. You m ay use th is page and continue on th e back of  is page. Ad(htional paper will be provided i t you need it, ju st raise your hand.

125

D enrity/A rchim edes'; C on cep tu al Q a estio n s 1.

Place the letter of the correct anawer on the scantron sheet. A 10 kg object h as twice the density' of water. Compared to 10 kg of water, its volume is a. as much b. h a lf as m udi c. twice as much d. less

2.

When the above m entioned object is suspended in w ater its m ass will appear to be a. 3.33 kg b. 5 kg c. 10 kg d. none of these

3.

Two vases of different shapes each contain a fîsh. In the position shown, the fish th at will feel the greatest pressure is a. A b. B c. both experience the same pressure d. can't tell

4.

The answer to #3 above is because: a. the w eight of w ater is greater in vase B b. fish A is n earer to the bottom of the vase c. both fis h are a t the same depth d. A's tank is a t a higher level

5.

B

A pebble is sinking to the bottom of the lake. W hen is the buoyant force greater? a. A b. B c. C d. buoyant force is equal a t all levels ^ A B

6.

This follows from the fact th at a. pressure increases w ith depth b. the same w eight of w ater is displaced a t any depth c. the w ater is more compressed with increasing depth d. B provides a m oderate answer- sort of an average

^

O O

^ __

'

7.

A certain force is required to keep a block 2 m beneath the surface of water. W hat force is required to keep it 4 m deep? a. zero b. the same c. twice a much d. four tim es as much

8.

This is because a. pressure increases w ith increased depth b. it displaces th e same weight of water a t any depth c. the block floats d. surface tension doesn't act beneath the surface

9.

A cubic m eter of lead which w ei^is 10^ N is submerged in w ater. The buoyant force acting on it is about 10* N a. the blodc loses h alf its apparent weight when suspended in w ater b. the block displaces 10^ N of water c. the volume of w ater displaced is one cubic m eter d. block loses twice its apparent weight when in w ater

10.

P art of a w rick from a ship weighs 500 N. I t displaces 200 N of fluid. The buoyant force acting on it is 200 N. From tbi« we can see th a t th e buogmnt force acting on it is equal to the a. weight of th e submerged obgect b. volume of fluid displaced c. difference between the weight of the object and the weight of the fluid d. w e i^ t of fluid displaced

126

11.

A rock is submerged in w ater and displaces a volume of w ater which is a. greater th an volume of stone b. less than the volume of stone c. equal to the volume o f th e stone d. zero

12.

The standard kilogram is a platinum-iridium cylinder 39 mm in height and 39 mm in diam eter. W hat is th e density of the m aterial in a. 21.4 b. 19.3 c. 13.6 d. 10.7

13.

In a large tank containing a liquid, the hydrostatic pressure at a given depth is a function of which of th e following? a. depth b. surface area c. liquid density d. A and C

14.

A ping pong ball has an average density of 0.084 g/cm^ and a diam eter of 3.8 cm. W hat force would be required to keep the ball completely submerged under water? a. 1000 N b. 0.788 N c. 0.516 N d. 0.258 N

15.

When ice floats in w ater, about 10% of the ice floats above the surface of the water. There is some ice floating in a ^ a ss of water. W hat wül happen to the water level as th e ice m elts? a. The w ater level w ill rise 10% of the volume of the ice th a t melts. b. The w ater level will rise, b u t not as much as the 10% indicated. c. The w ater level will rem ain unchanged. d. The w ater level wül become lower.

16.

Atmospheric pressure is 1.0 x 10^ N/m^ and the density of air is 1.29 kg/m ^. If the density of the a ir were constant as you go up, calculate the height of the atmosphere needed to produce this pressure. a. 7850 m b. 77,000 m c. 1260 m d. 10,300 m

17.

A large stone is resting on the bottom of a swimming pool.The normal force of the bottom of the pool on the stone a. is equal to the w eight of the stone. b. is equal to the w eight of the w ater displaced. c. is equal to the sum of the weight of the stone and the weight of the displaced w ater. d. is equal to the difference between the weight of the stone and the w eight o f the displaced w ater.

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ArchimedesVDensi^ Problems. ShowaU work. N am e:______________ S tu d en t #:

Cla ss L ectu re tim e :__

1.

A piece of m etal, w ith a density of 4.69 and a m ass of 1500 g, is subm erged in a container of oil, w ith a density of 0.75 g/cm^ . W hat volume of oil does th e m etal displace?

2.

A spring balance which registers in u n its of gram s is attached by a string to th e piece o f m etal w ith a density of 4.69 ^cm ^ and a m ass of 1500 g subm erged in a container of oü w ith a density of 0.75 g/cm^ . The balance w ill register w hat reading w hen the m etal is subm erged.

3.

A block of wood, w ith a m ass density of 0.50 g/cm^ and m ass of 1500 g floats in a container of oil, w ith a density of 0.75 ^cm ^. The balance w ül reg ister w hat reading w hen th e wood is submerged.

4.

W hat volume o f w ater is displaced by a subm erged 4.0 kg cylinder made of solid iron? (iron density = 7.86 x 10^ k^m ^ and w ater density = 1.0 x 10^ k^m ^)

5.

L ^ e n d says th a t Archimedes, in determ ining w hether or not th e king's crown was m ade of pure gold, m easured its volume by th e w ater displacem ent m ethod. If th e density of gold is 19.3 g/cm^ and th e crown's m ass is 600 g, w hat volume of w ater would be necessary to prove th a t it is p u re gold?

6.

A solid rock, suspended in air by a spring scale, has a m easured m ass of 9.0 kg. W hen th e rock is submerged in w ater, the scale reads 3.3 kg. W hat is the d en sity of th e rock? (w ater density = 1000 kg/m^)

128

Archimedes’/Density: Mental Model Name:_______________Student#:_____ Class time: W rite everything th a t you know about A rchim edes’ Principle and density. Include anything th a t m ay help illu stra te your knowledge. U se th is page and continue on th e hack of th is page. I f you need more paper, raise your hand and it will be provided.

129

H eat: C on cep tu al Q u estion s P la ce th e le tta r o f th e co rrect a n sw er o n th e sca n tro n sh eet. 1.

Which of the following best describes a substance in which the tem perature rem ains constant during an inw ard heat flow? a. gas b. liquid c. solid d. substance undergoing change of state

2.

H eat flow occurs between two bodies in therm al contact when they differ in w hat property? a. m ass h. specific heat c. density d. tem perature

3.

A falling 500 kg object is attached by a rope through a pulley to a paddle wheel shaft w hidi is placed in a w ell-insulated tank holding 25 kg of w ater. The object, in being allowed to fall, causes the paddle wheel to rotate to chum the water. If the object falls a vertical distance of 100 m a t constant speed, w hat is the tem perature change of the water? (1 kcal = 4186 J) a. 19600 OC h. 4700 °C c. 4.7 °C d. 0.8 °C

4.

A 0.003 kg lead bullet is traveling a t a speed of 240 m/s when it embeds in a wood post. If it is assum ed th a t h alf of the resultan t h eat energy generated rem ains w ith the bullet, w hat is the increase in tem perature of the embedded bullet? (specific heat of lead = 0.03 kcal/kg°(]) a. 115 b. 137 c. 230 d. 259

5.

A waterfall is 145 m high. W hat is the increase in tem perature of the water a t the bottom of the falls if all of the initial potential energy goes into heating the water? a. 0.16 OC b. 0.34 °C c. 0.69 d. 1.04 °C

6.

W hat is the tem perature increase of 4.0 kg of w ater when heated hy a 800 W immersion heater for 10 min? a. 56 OC b. 51 OC c. 28 °C d. 14 °C

7.

A 50 g cube of ice, initially a t 0 degrees C is dropped into 200 g of w ater in an 80 g aluminum container, both initially a t 30 degrees C. W hat is the final equilibrium tem perature in degrees CT? (specific heat for alum inum is 0.215 cal/g°C and Lf = 80 cal/g) a. 17.9 h. 9.4 c. 12.1 d. 20.6

8.

If heat is flowing from a table to a block of ice moving across the table, which of the following m ust be true? a. T te table is rough and there is friction between the table and ice. b. The ice is cooler than the table. c. The ice is changing phase. d. All three are possible, b u t none is absolutely necessary.

9.

As I use sandpaper on some rusty m etal, the sandpaper gets hot. a. H eat is flowing firom th e sandpaper into the m etal. b. H eat is flowing from th e m etal into the sandpaper. c. Friction is creating the heat. d. H eat is flowing from my hand into the sandpaper.

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10.

A 120 g block of copper is ta k p n 6om a k iln and carefully placed in a beaker containing 300 g of watmr. T te w ater tem perature rises from 15 degrees C to 35 degrees C. Given specific h eat of copper is 0.10 cal/g°C, w hat is the tem perature in degrees Celsius of th e kiln? a. 500 b. 360 c. 720 d. 535

11.

In a doud formation, w ater vapor turns into water droplets which get bigger and bigger u n til it rains. This will cause the tem perature of the a ir in the douds to a. get w arm er b. get cooler c. stay the same d. there is no air in douds

12.

Find th e final equilibrium tem perature in degrees C when 10 g of m ilk a t 10 degrees C is added to 160 g of coffee at 90 degrees C. (Assume specific heats of coffee and milk are the same as water and neglect the h eat capadty of the container). a. 85.3 b. 77.7 c. 71.4 d. 66.7

13.

How m uch heat energy is required to vaporize a 1 g ice cube a t 0 degrees C? The heat of fusion of ice is 80 cal/g. The heat of vaporization o f w ater is 540 cal /g. a. 620 cal b. 720 cal c. 820 cal d. 1 kcal

14.

A container of hydrogen gas has the same tem perature as a container of denser nitrogen and denser oxygen gas. The atoms having the greatest average kinetic energy are the a. hydrogen b. oxygen c. nitrogen d. all the same

15.

When an iron ring becomes heated by a flame, the hole becomes larger which follows firom the fact th a t a. expansion takes place inward toward the center of the ring as well as outward b. expansion takes place in all directions c. the surrounding air and the iron expand a t different rates d. the center only expands outward

16.

When a solid changes to a liquid and then to a gas, energy is a. absorbed b. released c. decreased

17.

Dew on the grass results fiom a. fast moving molecules b. evaporation c. the pressure of the atmosphere on w ater vapor d. the slowing down of fast moving w ater molecules

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d. latent

Heat: Problems. Show all work. N am e:______________ S tu d en t #:

Cla ss L ectu re tim e :__

1.

A 20 g object h as w hat specific h eat if its tem peratu re increases by 5 ® C w hen 20 cal of heat are transferred to it?

2.

A 200 g m ass of m etal w ith a specific h eat of 0.30 cal/g^C, initially a t 90 degrees C, is placed in a 500 g calorim eter in itially a t 20 degrees C w ith a specific h eat of 0.10 cal/g^C. The calorim eter is filled w ith 100 g of w ater in itially a t 20 degrees C. Once th e com bination of m etal, calorim eter and w ater reach equilibrium , w h at is the final tem perature?

3.

A 0.003 kg lead bullet is traveling a t a speed o f 240 m/s w hen it em beds in a block of ice a t 0 degrees C. I f all th e h eat generated goes in to m elting ice, w hat quantity of ice is m elted? The specific h eat of lead is 0.03kcal/kgC, the la ten t h eat of fusion is 80 kcal/kg and 1 kcal = 4186 J.

4.

A fia t pan container holds 200 g of w ater. If over a 10 m in. period, 1.5 g of w ater evaporates firom th e surface, w h at is the approxim ate tem p eratu re c h a n ^ of the rem aining w ater? (Ly = 540 cal/g)

5.

Iced te a is m ade by adding ice to 1.8 kg of h o t te a , initially a t 80 degrees C. How many kg of ice, initially a t 0 degrees C, are required to b rin g th e m ixture to 10 degrees C? (Lf = 80 kcfd/kg). Assume the specific h ea t capacity of tea is th e sam e as th a t of w ater.

6.

A 100 g piece of copper, in itially a t 95 degrees C, is dropped into 200 g of w ater contained in a 280 g alum inum calorim eter; the w ater and calorim eter are initially a t 15 degrees C. W hat is th e final tem p eratu re of th e system? (specific heats of copper and alum inum a re 0.092 and 0.215 cal/g^C, respectively)

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Heat: Mental Model Name:__________ Student# : _____ C^ass Lecture Time: W rite everything you know about h e a t Include anything th a t m ay help you illu strate your knowledge. U se th is page and continue on th e back of th is page. I f you need m ore paper, raise your hand an d it will be provided.

133

Mental Model Template Points of Reference Sentence number

CO

4k

Agent

Action

Object

Receiver

Points of Observation Goal/explanation

effect

time

location

conditon

APPENDIX C: Learning Cycles Graphing Laws of Motion Motion of Ball on Incline Motion of Ball on S teeper Incline Motion of Falling Ball V ectors Friction C ircular Motion E nergy The Balancing Act Collisions and th e Rules th a t Govern Them D ensity Archimedes’Principle Specific H eat in Solids

135

G raphing Introduction. This activily w ill allow you to gain experience in graphing, in describing graphs, and in using equations to describe graphs.

Ezplarati
3. Now graph th e x-values along th e horizontal axis and th e y-values along the vertical axis. Label th is graph: G raph A: 2x versus x. 4. Describe the shape of th e graph.

PartB. 5. Select six integers betw een 0 and 10. Record in the x-column. 6.

Square each of th e x-values. Record in th e y-column.

7. Now graph th e X and y values. 8 . Describe th e shape of th e graph.

136

P a r te . 9. Select six integers betw een 0 and 100 th a t have integer square roots (such as 49 since square root of 49 is 7). Record th e values as x’s an d th e ir square roots as y’s.

10. G raph th e X and y-values. 11.

Describe th e shape of th e graph.

P artD . 12. Select six in t^ e r s betw een 0 and 20. Record as x-values. 13. To obtain th e y-values, ta k e th e reciprocal of th e x-value.

14. G raph th e X and y-values. 15. Describe th e shape of th e graph.

137

C om cqxtual In ven tion . 1 . W ere th e graphs from p a rt A, B, C, and D sim ilar? In w hat ways? Explain.

2. In your own words, describe th e y=2x graph.

3. W hat do you th in k th e shape o f a y ^ x graph would look hke? G raph it on th e sam e piece of graph paper as th e y= 2x graph.

4. Describe a y=Nx graph? (N is a n integer)

5. In your own words, describe a y=x^ graph.

6.

In your own words, describe a y= squareroot of x graph.

7. h i your own words, describe a y= 1/x graph.

138

8 . Now, if you w ere to look a t a graph (and it was one of th ese four types), could you intelligently guess a t 6 e A rm of the graph’s equation? E aplain how or how not.

Ezqmnmon. 1.

For the following: w rite th e form ofthe equation descrihing th e graph.

y

y

X

X

b.

a.

y

y

X

X

d.

c.

139

2. Each student m u st p u t one paperclip on th e electronic scale and record th e total m ass on th e board. P lot th e # of paperclips on th e horizontal axis and the total m ass on th e vertical axis. Describe  e graph. W rite an equation describing th e graph.

3. W hat is th e slope of th e graph?

4. Look a t the g rap h and then look a t th e average m ass of one paperclip. How does this m ass com pare to th e slope of the graph?

5. In your own words, teU how you can obtain the specific equation of a straight line in term s of x and y only. Be sure to define w hat x and y are in your equation.

140

L aw s o f M otion E xp loration 1. Equipm ent: shoebox, scissors, rubber ball M ake a tbree-sided box o u t of th e m ilk carton w ith th e scissors. back

front 1. Place the rubber ball in th e box next to th e back wall. P ush th e box forward. W hat happens to th e ball w hen th e box is moving?

W hen the box is m oving is th e ball moving? How can you tell?

2. Now place the ball n e a r th e fiu n t of th e box. P u sh the box forw ard. W hat happens to the ball as th e box begins to move? W hat happens to th e ball after th e motion has begun for some time? W hen the box is m oving is th e ball moving? How can you tell?

3. Now place the ball n ex t to th e back w all again. P ush th e box forw ard quickly, but stop it suddenly. W hat happens to th e ball after you stop th e box? Try it again. Does th e baU move? If it does in w hat direction?

141

4. From your observations, w rite some general statem ents ab o u t th e m otion o fth e ball.

C on cep tu al In v en tio n 1. 5. W hat happened to th e ball w hen th e box w as still for several m inutes?

6.

W hat happened to th e ball w hen th e box is first pushed forw ard?

7. A fter th e initial m otion of th e box, is th e ball moving? How can you tell?

îf it is moving, how fa st is it moving? 8.

W hat happens to th e ball w hen th e box is stopped suddenly?

9. In w hat direction does th e ball move when the box is stopped?

Complete th e following sentences. 10. A ball a t rest continues to be a t _______ unless 11. A ball in motion continues to be in __________ in , ___________________ u n le ss_____________________ 12. A push or pull is called a 13. Sentence 10 and 11 above are statem ents of

142

Expansion 1. Recall th e m ovem ent o f th e ball fi*om question 2. R ecall th e movement of th e ball h"om question 3. Ih each case, how does th e m otion of th e ball compare w ith th a t of th e box? In w hat direction does each move?

When som ething has a tendency to resist a change in its m otion it is said to have inertia. In ertia is th e tendency of an object to re s is t changes in its motion. N ew ton's F irs t Law is sometimes called th e law o f inertia. Now u sin g th e new term in ertia w rite a sentence or two explaining th e motion of the ball in th e box.

Equipm ent: compass (draw ing type), penny, toy car, m etric ru ler Draw a circle of radius 10 cm on a piece of paper. T his vyill be the road for our car. P u t th e coin on top of th e car. Quickly push th e c a r around the road. 14. W hat object or objects feel a force? 15. W hat is the path of th e car? 16. W hen slowly pushing the car suddenly stop th e car. W hat objects or objects feel a force? 17. W hat happens to th e coin? W hat is its path?

18. W rite a statem ent explaining the motion of th e coin using Newton's F irst Law.

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Eaplorati
1. Place one m ass in th e box. P ull on th e spring scale so th a t th e box moves. W hat happens to th e spring scale? W hat value does it read?

Record this value in th e d ata table provided. D ata Table 1 # of m asses Scale reads 1 2

______ ______

3

______

2. Repeat, b u t pay atten tio n to how fast th e box moves. Once you can judge how fast it moves, place another m ass in the box. Pull on th e sp rin g scale so th a t the box moves as fa st a t th e end as it did before. Is it h ard er or easier to pull? Record th e scale reading in D ata Table 1. W hat happens to th e spring scale? 3. Place the th ird m ass in th e box and repeat. Record th e value of th e spring scale. Again, be su re to have th e box moving as fast a t th e end as it was before.

144

C on cep tu al In v en tio n 2a. 4. W hat can you say abou t th e num ber of masses and th e scale readings in questions 1-3 above?

5. W hat does th e sp rin g scale reading represent? W hat does th e num ber of m asses in th e box represent? 6.

W hat can you say ab o u t these two things from #5?

E xp loration 2b. 7. Now w ith one m ass in th e box, pull so th a t the spring scale is twice w hat it w as before. You m ay need to practice several tim es to pull so th a t the spring scale read s tw ice w hat it did. Use th e w ords f a s t, v ery fast, very very fast, slow, v ery slow, or very very slow to describe th e m otion of the box. Record your descriptions in D ata Table 2. D ata Table 2 mass speed a t beginning speed a t end Scale reading Speedchange

C on cep tu al In v en tio n 2b. 8.

How fast was th e box and m ass moving ju st as you first began to puU it?

9. Tell how m uch th e speed of th e box and the m asses changed from th e tim e th a t you first began p ulling on them to the end. Use th e term s alot, a little, very little, or none to describe how much th e speed changed fi-om beginning to end. W rite your descriptions in D ata Table 2.

10.

W hat does th e scale reading represent?

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11. W hat can you say about th e force th a t you exerted and how m uch th e speed of th e m asses changed?

E!z]Muision2.

Equipm ent: identical books, spring scale, strin g, scissors 1. Tie a string around one book. Hook th e spring scale on th e string at th e center. Pick up th e book w ith the spring scale. H old it still and record th e value of th e spring scale in th e data table. D ata Table # of books

Scale reading

Prediction 1

2. Predict w hat th e value of the spring scale w ill be w ith two books. Record your prediction in th e d ata table. Now place a second book w ith th e first and re-tie th e string as before. Raise the book off of th e table. Holding it still, record the value of th e spring scale. Is it close to your prediction?

3. Now predict w h at th e value of the spring scale will be w ith three books. Record your prediction. Place a third book w ith th e first two and record th e value of th e spring scale. 4. W hat can you say about the num ber of books you are holding and the value on the spring scale?

5. Is it easier to lift 1 book, 2 books, or 3 books? Why? W hat force are you pulling up with w hen you a re holding up one book? Two books? Three books? Why?

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For Further Expansion 2. Equipm ent: 2 spring scales, book, desk or table, string, scissors C ut a string so th a t you can tie it around a book. Tie th e strin g around a book and hook two spring scales on opposite sides of the book. Leave th e book on the table. W ork in pairs, w ith one stu den t pulling on one sp rin g scale. Pull w ith th e sam e force on each spring. T alk to your p artn er to be su re th a t you are each pulling w ith th e sam e force. Describe w hat happens to th e book.

Does it move while you are both pulling w ith the same force?

W hat happens if one of you lessens th e pulling force or lets go? W rite a sentence or two describing w hat you observed.

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Exploration 3. Equipm ent: skateboard,‘medicine ball’ W ork in p a irs so th a t one is a l i ^ t student and one is a heavier student. One student carefully stands on th e skateboard, th is is th e throw er. The other stands ab o u t 2 m aw ay and is th e catcher. The stu d e n t on th e skateboard is to throw th e basketball to th e other stu d e n t 1. D escribe w h at happens to th e throw er and th e ball.

2. R epeat th e throw , but this tim e throw the ball h ard er. D escribe w hat happens.

3. Com pare th is throw w ith th e first one.

4. Switch jobs so th a t the throw er is the catcher and th e catcher is now the throw er. R epeat th e above procedure. W hat th in g s are th e same and w hat things are different?

C on cep tu al In v en tio n 3. 5. W hat can you say about th e direction in which th e b all w ent com pared w ith th e direction in which the throw er w ent?

6.

W hat did th e throw er do to the ball in th e act of throw ing it?

7. W hat caused th e throw er to move as he did after th e throw ?

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8.

W hat general sta tem en ts can you m ake about th e hall and th e throw er?

E x p a n sio n s. Equipment: skateboard, waU Stand on th e sk atebo ard so th a t you can push on a wall. W hat hap pens when you push on th e w all?

Are you exerting a force on th e w all when you push on it? W hat m ade you move as you did?

You are now read y to com plete th e problems assigned in your tex t d ealin g with N ewton’s Law s.

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Afotion of BaU on Incline Introduction: W hat is im p o rtan t to be included in a description of th e motion of a ball rolling down an incline? T his investigation will allow you to learn how to describe such m otion u sin g physics term s. E xploration. 1. Place th e wooden V -trim to the incline apparatus (w ith th e “0” a t th e lower end). A djust th e incline to 30 degrees. 2 . Note on th e grooved board th a t there are m arks denoting: 60.00 cm, 70.00 cm, 80.00 cm, 90.00 cm, etc.. These are the distances from th e end of th e ramp.

3. U sing your pencil as a stop, release the ball from th e 60.00 cm m ark and record in th e tab le th e tim e it takes the ball to reach th e end of the ram p. To ensure greater accuracy, rep ea t the process 2 more tim es. Now average th e tim es and record u n d er th e tim e column. 4. R epeat Step 3 for 70.00 cm, 80.00 cm, 90.00 cm, 100.00 cm and 110.00 cm distances. ______________________ Table 1.________________________ : distance

tim e l

time2

timeS

tim e (avg)

?

j

5. Look a t the d a ta for p attern s. W rite a sum m ary of w h at you observe from Table 1.

150

C onceptual In ven tion . 1.

G raph the distance versus th e tim e.

2.

W hat does th e graph look like? D escribe it.

3. As th e tim e increases, w hat happens to the distance traveled?

4. From your graph, w hat is happening to the ball?

5. Go back to Table 1 and calculate th e average velocity for each of th e ball’s trips. Record it in th e “?” column in th e table. 6.

Do your calculations from #5 above agree with your answ er to #4? Explain.

7. Plot a graph of th e average velocity versus the tim e (avg). Describe th is graph.

151

8.

A fter you have draw n th e best fit lin e through th e d ata points, exam ine thefollowing; Choose 2 points th a t have a difference in average velocity of 10 cm/sec. ) ^ a t is th e tim e in terv al betw een th ese 2 points? Chose 2 other points th a t have a difference in average velocity o f 10 cm/sec. W hat is th e tim e in terv al betw een th ese 2 points? 9. W hat can you say about th e re su lts of #8 above?

10. Recall w hat you know about lin e ar graphs. Is th e re a relationship betw een the chmige in average velocity, tim e, an d slope?

If so, w rite the equation involving all th ree quantities.

11 ,

W hat is the nam e for the slope?

W hat happened to th e hall going down th e incline? (Use your new term s.)

152

Elxpansicm. 1.

Calculate th e slope of the graph for th e ball on th e incline.

2. W hat is th e special nam e for th e slope of th is graph called? 3. W rite a definition for acceleration in term s of th is investigation.

4. W hat are th e u n its for acceleration? 5. U sing the equation th a t you developed fi*om #10 above, solve th e following: A car is advertised to trav el fi*om 0 to 60 m i/hr in 5 seconds. W hat is th e acceleration o f such a car?

6.

In w riting and u sing your new terminology, describe w hat happened to th e car in the problem #5 above.

153

Motion of BaU on Steepor Incline Inlxodnction: F u rth er eiq)erim entation w ill allow you to practice describing th e motion of th e ball rolling down th e incline. E ^ d oration . 1.

Repeat Investigation 1 w ith th e incline set a t 45 degrees. Record all of your d ata in Table 2. Table 2 distance

timel

| time2

j time3

j time (avg) i avg. velocity

2. Plot th e average velocity v ersu s the tim e and obtain th e acceleration o f the ball rolling down the incline. C onceptual In ven tion . 1. Describe how th e acceleration of the ball varied from th a t of previous incline.

2. Why do you think th a t th is is so? W hat is your evidence?

3. Describe the velocity change in any 0.200 second interval of tim e. P ick 2 other 0.200 second intervals to check. Be sure to select points ON THE LINE th a t you drew (NOT d ata points). Why?

Is the velocity change the sam e or different?

154

4. W hat is changiiig as th e ball rolls down th e indine? D escribe w hat happens to th e velocity of th e ball as it goes down th e incline. How does it compare to the velocity of th e ball on th e previous incline?

E^qumston. 1. W hat do you th in k would happen to th e acceleration of th e ball if th e incline were inclined a t 70 d ^ re e s? 90 d ^ re e s?

2. From your answ er from # 1, which ball would be going faster a t th e bottom of the ram p, one inclined a t 70 degrees or one inclined a t 90 degrees? E aplain why.

3, Use equations to explain your answer in #2.

155

M otion o f a FaD ing BalL In irod n ction . You have described th e motion of a hall on a n incline and even postulated w hat would happen if th e incline were a t 90 degrees. Now you w ill drop th e ball and describe its motion. E a^loration: 1. Assemble th e tim er app aratus as instructed. W hen th e hall is released a t the top the tim er b^[in s counting. I t stops counting when th e ball h its th e tim er pad. Pressing th e rese t button allows tim ing for additional tria ls. A sk your instructor if you need assistance w ith the apparatus. H int: T ry distances 6 -om 40 -140 cm.

2. Using th e equipm ent, obtain the acceleration of th e baU. Rely upon your experience from th e firs t tw o investigations to do so. Here is a blank table for your data. Be sure to in se rt headings for th e columns. Table 3.

C onceptual In ven tion . 1.

Explain all the steps you took to obtain th e acceleration of th e ball.

156

2. Plot th e d istan ce th e ball fell (vertical axis) versus th e tim e (avg) of fall squared. W hat is Hie slope of th is graph? Discuss.

3. W rite an equation th a t illustrates th is relationship betw een d istan ce and tim e 2 -

4. Does th e value for th e acceleration of th e ball seem reasonable com pared to w hat you got from th e acceleration of th e ball for th e two previous investigations? E xplain.

5. Since the ball w as freefalling, describe the motion of the ball. In other words, explain w h at happens to th e ball as it falls.

6.

W hat do we call th e acceleration of a falling ball?

7. W rite th e form ula for th e distance, acceleration, and tim e for a n object freely falling from rest.

157

E^wmaiom. 1. Would you expect a heavy ball and a sm all ball to fall w ith th e sam e acceleration? Collect data to support your answ er. Again, here is a blank d a ta tab le for your use. Table 4.

W bat is your conclusion? (Does a heavy ball and a lighter ball fall w ith th e same acceleration?). Ju stify your answ er.

E xpansion P rob lem s. 1. A rock is dropped off of a building th a t is 100 m tall. Find bow long it takes it to b it th e ground using the accepted value for the acceleration o f an object in freefall (9.8m/s2).

2. If it takes a rock 3 seconds to b it th e ground when dropped from th e top of a cliff, how tall is th e cliff?

You should be ready to do the problems in Ch. 2. Begin w orking on them !

158

V ectors Introduction. You have probably added num bers linearly, for example: 2 + 3 = 5, 3 + 4 = 7. Could 2 + 3 ever equal th e square root of 13? Could 3 + 4 ever equal 5? You will exam ine such cases. Equipm ent: R uler, force apparatus, tension scales E xploration. Use a spring scale to pick up a lOOg weight. W bat is th e spring scale doing to allow you to lift th e weight?

W bat does th e force of th e spring scale represent or m easure?

If you were to lift 20 lbs, in physics term s w b at are you doing to th e object?

Now set up th e force apparatus to look like th is. D ata 1 Fi

I

P2

Sketch bow your app aratus will look for force 1 and force 2, being careful to include the values of F i and F 2 as read from the tension scales. Be sure to m ark th e locations of F i and F 2 on your paper. Record th e values in D ata Table 1.

159

Now we are going to look a t a m ore com plicated exam ple on D ata 2 and use three forces. A djust th e pulleys and th e angles betw een th e forces so th a t the ring is exactly in th e center. Record th e values o f F 2 , an d F g . Be sure th a t you m ark th e location of th ese forces on th e p aper th a t you place underneath th e force scale apparatus. D a ta 2 Fi

F2 F3 Once the forces are recorded and th e positions of th e arm s are located ta k e a protractor and m easure th e angle betw een force 1 and force 2 , th e angle between force 2 and force 3, and th e angle betw een force 3 and force 1. Record your resu lts in D ata Table 1. D ata T ab le 1 IDa to] F o n e in

J A i^ _

force2=

I

________

2&1 =

I--

2 forcel= force2= force3=

2 ^ 3&1=

C onceptual In v en tio n . 1. Observe the D ata 1 diagram th a t you drew . Describe how Force 1 and Force 2 are acting on th e ring. How are th ese forces related to one another?

2. Summarize w h at you think D ata 1 is tellin g you about force 1 and force 2 .

3. Describe how force 1, force 2, and force 3, on D ata S et 2, are related. Describe how the forces are acting in th e directions th a t th ey are acting. Be sure to explain th e angles involved.

160

4. Summarize what you think the Data from Set 2 are telling you.

5. In D ata set 1 force 1 is pulling upw ard. In D ata se t 2 force 1 is pulling upw ard. In D ata set 1 th e re is a force 2 pulling dow nw ard, b u t in D ata set 2 th ere are 2 forces pulling it a t angles aw ay from one another. How are force 2 and force 3 relatW to force 1?

Could you call th e com bination of those some force? H so w h at is th a t force?

6.

W hat would be the direction of th e combination of force 2 and force 3?

7. How is th is combination of force 2 and force 3 related to force 1?

8.

Now use D ata 1 to draw a scale diagram of those d ata. F or a scale diagram a certain length rep resen ts a certain am ount of an o th er quantity. For example; 1 cm m ay rep resen t 200 g of w eight, 2 cm m ay rep resen t 400 g of weight. U sing D ata 1, draw a scale diagram of force 1 an d force 2.

9. How are force 1 and force 2 related to each other?

161

10. Now draw a scale diagram of D ata set 2. W ith F i being th e len g th of force 1 converted into cm, F2 being th e length of force 2 converted in to cm, and Fg being th e length o f force 3 converted into cm on your scale.

11. Once you have your scale draw ing drawn, th en draw a parallelogram using F2 and Fg as th e sides of your parallelogram . Draw th e vector from the intersection of th e th re e forces down to the opposite side of th e parallelogram. W hat do you th in k th is vector represents?

12. Explain w hy th is vector can be called th e resu ltan t force of F 2 and F 3 .

13. How does th is re su lta n t force relate to force 1?

162

14. Describe what you think a vector is.

F.-icpnm rinii.

Read your tex t book page 55 th ru page 60. Com plete questions: 1 ,3 ,4 , 6 on page 75 in the tex t book. Furtherm ore, answ er th e questions below. 1. Explain w hat it m eans to say th e m agnitude o f a vector is a scalar.

2. S tate which of the following are vectors and w hich are n o t vectors. For example, classify th e following: force, tem perature, th e am ount of w ater in a can, the w eight of a book, th e height of a building, th e velocity of a sports car, and the age of th e universe.

3. Now th a t you have studied vectors experim entally and have read about vectors experim entally, sum m arize th e steps th a t you ta k e to add vectors using components. In oth er words sum m arize section 3.3 of your tex t book in vDur own words. Feel free to choose forces as an exam ple to explain your sum m arization of the forces.

163

Fricti
2. Why do you think th e m otion is such? 3. M ass a block w ith th e spring scale. Record in D ata Table 1. 4. Take a block and attac h a spring/tension scale so th a t you can pull th e block w ith th e scale so th a t the block has a constant speed. R ecord th e value in gram s fr-om th e tension scale in d ata tahle 1. Tape 100 g to th e top of the block of wood and repeat. 5. Continue too add 100 g to th e block and rep eat step 4 th ree m ore tim es. D ata Table 1._______ i T otal M ass=M

Tension=T

i. . . .

6. Plot a graph o f T versus M. 7. Determ ine th e slope of th e graph. slope = _________

8. Does the slope of th e g rap h have any units?

164

9. W hat does it m ean if som ething doesn’t have any units? Is it a force, a m ass, etc?

C oncep tu al In v en tio n . 10. W hat does th e force th a t you read on th e tension scale represent? H in t: Would th is force change if you pulled th e block on ice? On rubber? W hat do you think?

11. W hat is th e equation of the line th a t you graphed?

12. W hat does th e slope of the line rep resen t?

13. Use your new terminology in a sentence describing the equation of th e line th a t you graphed.

14. Draw a free body diagram for th e situ atio n in which you are applying a force through th e tension scale so th a t th e block moves a t constant velocity across th e table.

165

EbqpanaioD. 15. Find th e coefficient o f kinetic friction for th e block on th e floor using th e equation (only one d ata point) instead of obtaining it finm a graph. T hen find th e coefficient of kinetic friction for th e block on flie floor by th e m ethod th a t m ade use of th e graph. W hich one do you th in k is more accurate? Why?

Coefficient of kinetic friction for wood on tile (eqn. method) =.

Coefficient of kinetic friction for wood on tile (slope method) : A d ata table is provided below: to ta l m ass

tension

How do the two coefficients compare?

166

16. Read the section in your book about friction on an inclined plane as a block ju s t begins to slide. Be su re to draw here th e free body diagram s so th a t you understand how th e y obtained th e expression th a t the coefficient of starting friction is th e ta n g en t o f th e angle a t which it begins to slide.

17. Now incline th e lab tab le and obtain th e coefficient of sta rtin g friction for the lab table and wooden block. How does it compare to th e coefficient of kinetic friction obtained earlier? Com pare w ith m em bers of th e class. Is one always larger th a n th e other?

18. Now read the re st of th e ch ap ter on friction (Ch. 4) and w ork th e assigned problems.

167

C irc id a rM o tic m E q o ^ m e n t: C ircular m otion ap paratus, strin g and rubber stopper Eiqdofraticm . 1. Slowly rotate th e ap p aratu s. D escribe w h at happens to th e m ass.

2. Remove th e spring from th e larg e m ass an d slowly ro tate the a p p a ra tu s. 3. Describe w hat happens to th e m ass.

4. W hat effect does th e sp rin g have on th e m ass w hile it is in motion? 5. Now tw irl a strin g w ith a ru b b er stopper on th e end of it. W hat effect does th e strin g have on th e stopper?

6. S tate your findings about an object in circular motion. In your explanation, be sure to answ er th e question: w hat it is th a t m akes a n object move in a circle?

C onceptual In v en tio n . 7. W hat is necessary for an object to move in circular motion? W hat is your evidence?

8. U sing the new term inology, sum m arize your findings.

168

9. In w hat direction does th is force act? How can you te ll o r how do yon know? Tell w h a t th e spring and string do.

10. W hat o th er variables m ight affect th is force? L ist them .

11. D iscuss/tell how you m ight te st to see if these variables affect th e force th a t m akes an object move in a circle.

Eaq)ansiom. 1. W hat is it th a t keeps th e clothes in a w ashing m achine m oving in a circle? In w hat direction does th is act?

2. W hat is it th a t keeps your car moving in a circle as you tu rn a curve? (Hint: Think about turn in g a curve when there is ice on th e road.)

3. Using your knowledge th u s far about circular motion, explain w hy a pilot pulling out of a steep dive will t l a c k out". (H int: For th e sam e reason a car on an icy curve w ill fail to stay in a circular path.)

169

C en trip eta l F orce Eqnqsm ent: C ircular m otion apparatus, stopwatch, m asses, g rap h paper, scales E xploration. 1. TeU how you can determ ine th e velocity of th e rotating m ass. (H int: How can you find th e velocity of a ca r w hen the speedometer is broken.

2. S tate how th e centripetal force can be determ ined.

3. For the radii given, m easure th e tim e for 30 oscillations th e n u se it to determ ine the velocity. Find th e m ass needed to stretch th e sp rin g a distance equal to the given radius. Record in th e D ata Table 1. D a ta T able 1 1 radius dist. around once tim e a r o i^ d 1 14cm

YGlocd ty

centripetal m ass c e n trip e ta l force j

......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . {

\ 16cm..................................... 18cm : 20cm

.

_

1 i i

4. Calculate the distance around once for each radius and record in D ata Table 1.

5. Calculate th e period and record in D ata Table 1. 6. Calculate th e velocity and record in D ata Table 1. 7. Calculate th e centripetal force using the centripetal m ass and N ew ton’s Second Law. 170

8. Plot a graph o f cen tripetal force verses velocity. 9. Describe th e g rap h of Fc vs. v.

10. Plot a graph of centripetal force verses velocity squared. 11. Describe th e g rap h of Fc vs. v2.

C onceptual In v en tio n . 12. W hat does th e graph of Fc vs. v2 suggest?

13. Use your m athem atics knowledge to w rite an equation for th e Fc vs. v2 graph.

14. Now determ ine th e value of th e slope of your graph. Record it here:__________________ .

15. D eterm ine th e q u o tien t of the m ass of the ro tatin g bob and th e avg. radius of the circular o rb it Record th is quotient here:.

171

16. How does th e q u o tien t in #15 above compare w ith th e slope obtained in #14?

17. W rite a new equation for th e graph of Fc verses v2 using th is information.

18. S tate in your own w ords the relationships th a t you have found betw een th e variables.

E sp an sion . Read Section 7.4 th ru 7.7 in your text. W ork problems: 29,31,34,39.

172

E nergy Introduction. E xperim entation w ith th ese m aterials should enable you to leam about energy. E ^ lo ra tio n . 1. Take the fun dough and flaten it out so th a t it is about 3/4 to 1 inch thick. It needs to be 3 to 4 inches squ are to provide an adequate targ et. 2. Drop the sm all steel ball onto the fun dough from a height o f about 40 cm above Ihe fun dough. Drop th e large steel ball onto the fun dough from th e same height. Describe w h at happens to th e dough.

3. Drop the sm all ball from th e ceiling height and the large ball from a height of about 10 cm. Describe w h at happens to th e d o u ^ . Now, reverse th e two balls (sizes) and repeat. D escribe w hat happens to the dough.

4. Based upon your answ ers to 2 and 3, how does height affect th e am ount th a t the ball indents th e dough?

5. Based upon your answ ers to 2 and 3, how does mass of th e ball affect th e am ount th a t th e ball indents th e dough?

173

6. P redict how the doug^ w ill be indented when you drop th e large ball from a h e i ^ t of about 40 cm and you throw th e large ball from a height of 40 cm above th e dough. W hat is th e initial velocity of the ball th a t is dropped as com pared to thrown? Does th is give you an idea as to why you guessed th e predicted outcome? Eiq)lain.

7. Now be careful (don’t h u rt your lab p a rtn e rs) or b reak anything) and actually do #6 to see if you w ere correct in your prediction. W rite your conclusions here.

C on cep tu al In ven tion . 8. W hen lifting the sm all ball as compared to th e large hall (to the sam e height), tell which one requires more exertion (or work) on your p a rt

9. A ball th a t is dropped from a height of 40 cm re q u ire s tim es as m uch w ork to lift it to th a t height as a ball th a t was lifted and then dropped from a height of 80 cm. 10. A ball th a t is twice as heavy (or m assive) as another ball req u ires___ tim es as m uch work to lift it to 40 cm. 11. W rite your definition of work.

12. You did so much work on the steel ball in lifting it, w h at happened to this w ork w hen you let the ball go? W hat happened to th e ball as soon as you let it go? W hat happened to th e dough as tiie ball h it it?

174

13. W rite the definition of potential energy and kinetic energy in your own words.

14. Compare potential energy and work. In th is e^)erim en t, how are they related? (i.e., you gave the baU and it th en h a d ).

15. Compare th e potential energy and kinetic energy as th e ball fell. Assume th e ball had 10 un its of work done on it, and describe w h at happens to the 10 u n its as th e ball falls.

16. W rite th e variables th a t you think affect how much k in etic energy the ball has and how m uch potential energy th e ball has. (th in k about #2,3,4 & 7 or te st others yourself).

17. After th e class discussion, can you elim inate any of th e variables you listed, or add an y th a t you forgot to include? Explain.

18. W rite th e equation for kinetic energy and for potential energy Ehqum sion. Read C hapter 5 and do th e problems assigned.

175

The Balancing Act E quipm ent: m eter stick, m asses, pivot, knife edge, clam ps In troduction. To be in balance m eans th e sam e thing as to be in equilibrium . In th is investigation you w ill study abo ut equilibrium and w hat is called th e balance or teeter to tter as it m ay have been caüed when you w ere a child. A fulcrum (F) is ju s t a support pivot point. T he fulcrum will pivot on w h at is called a knife edge or pivot. Dleft

[

D r i^ t - 7 ^ ------

□

□

F

Wleft

W r i^ t

Figure 1

E xploration. 1. Balance the m eter stick alone. A djust the m eter stick on th e fulcrum so th a t the m eter stick is perfectly horizontal. To distinguish perfectly horizontal m easure th e distance th e rig h t end of th e m eter stick is from the table and the distance the left end of th e m eter stick is from th e table. If th is distance is th e sam e from th e m eter stick to the table on both ends th e n the m eter stick is perfectly horizontal. The balance point is th e location of the knife edge on th e m eter stick. Indicate the point of n atu ra l balance on the D ata Table 1. Data Table 1 Natural balance point of the meter stlck=_

Be sure to tig hten th e knife edge a t th is point on th e m eter stick because you will be using th is n atu ra l balance point throughout the re s t o f the investigation. 176

2. W ith th e pivot on a m eter stick a t th e n atu ral balance point, place a m ass on a clamp. Place an o th er mass on another clamp a t a location th a t balances th e stick. R^>eat 3 tim es for other m asses a t different locations. Record in D ata Table 2. D ata T able 2. 'IVial !Wleft in g

Dleft in an !Wright in g D ri^ t in cm

C oncep tu al In v en tion . 1. M ultiply W Left tim es DLeft. Do th e sam e for W pight tim es DP ight Record in d ata table below. TWal ;Wleft X Dleft [Wright x Dright

2. From th e above data table, can you w rite a general ru le for weights and their distances on a m eter stick a t its n atu ral balance point.

3. W hen on a teeter to tter, where m u st you place a big and a sm all child so th a t they can teeter to tter? Draw a sketch.

177

4. The product ofw eight versus distance from th e fulcnim is called torque. A torque causes a rotation which has a direction clockwise or counterclockwise. S tate th e direction of the torque or rotation for each o f th e m asses shown. H int; ^?iore all other m asses besides th e one for w hich you are determ ining the torque.

[

"T V

o

Ô m a ssl

m ass2

E ^M m sion. 1. W here m u st one place a 50 g m ass if a 200 g m ass is placed at 60 cm on a uniform m eter stick w ith a pivot point a t 50 cm?

2. Read Section 8.1,8.2, and 8.4. Do problems #4, 8, 9 ,1 2 ,1 6 , 21.

178

C o llisio n s an d T he R u les T hat G overn T hem Exploration. The following d ata w ere gathered by a com puter for your use. To obtain th e d ata, car 1 had a m ass of 10 kg and car 2 had a m ass of 20 kg. W hen th e two cars collided, th ey stuck together and traveled as one larger car of m ass 30 kg. O bserve th e data and try to come up w ith some ru le regarding th e m asses and velocities. The rule m ust w ork for each case. Note th e sign convention used: positive velocities are directed to th e rig h t and n ^ a tiv e velocities are dirâzted to th e le ft Draw a sketch noting th e directions of th e cars to show m e you understand. Sketch showing car’s direction/vel. before collision m ass carl=10kg , 3 .00m/8

maM c ^ 2 = 2 0 kg O.OOm/s

. 2.00m/s ; 4.00m/s : -2.00m/s

l.OOm/s l.OOm/s -S.OOm/s

after collision

cars combined=30kg l.OOm/s 1.33m/& 2.00m/s -2.67m/s

C on cep tu al In v en tio n . 1. W hat rule can you determ ine fits each case? Show below how th e ru le fits one of the cases .

2. W rite th is ru le in algebraic and in sentence form.

3. W rite a sentence using th e term momentum in th e rule.

179

4. Look a t th e k in etic energy of th e objects. Does th e kinetic e n e i ^ of all the objects before th e collision equal the kinetic energy of all of th e objects after the collision?

5. Why do you th in k th is is so?

6. The following d a ta w ere gathered by computer for two cars th a t collided head-on, b u t did no t stick together. Instead, they bounced off o f each other. Case 1. before 3m/s 10 kg

10kg

-2 m/s after 10 kg

10kg

3m/s

-2m/s Case 2. before 4kg

2 kg 3 m/s

-2 m/s

after 4kg -,3m/s

2 kg 4.6m/s 180

W rite a rule including m asses and velocities th a t explains th e collision of two objects th a t bounce off of each other. 7. Is this rule sim ilar to th e earlier rule?

8. Check th e kinetic energy. Is the kinetic energy of all of th e objects before the collision equal to th e kinetic energy of all objects after th e collision? W hy do you think this is so?

Eaqwmsion. 9. Summarize your ru les for conservation of momentum and conservation of kinetic e n e i^ fo r elastic and inelastic collisions.

10. Work on the m om entum problems in your textbook.

181

D en sity E quipm ent: Alum inum cylinder, lead cylinder, overflow can, balance, graduated c^inder E xploration. 1. M ass th e dry graduated cylinder. Record h e re :__________ M easure 30.0 ml of w ater w ith a graduated c)iinder. This represents the _____________ of th e w ater. 2. Mass th e 30.0 ml of w ater in the cylinder. Record th e m ass of th e w ater in grams. _______________ represents the m asses o f____________ ml of w ater. 3. Repeat #1 and #2 above w ith 25.0 ml and 40.0 ml of w ater. Record your results: 25.0 ml w ater mass=__________________ 40.0 ml w ater mass=__________________ 4. W hat can you determ ine from the results of th e exploration?

5. Do you th in k th is applies to different m aterials? Use the alum inum and lead object to find out. Subm erge th e objects in w ater to m easure th e ir volume, as you did in Archim edes' Principle. Record your findings below. _____ ml of aluminum has m ass=_________ g. ml of lead has mass=______________g. 6. Divide th e m ass and volume by the num ber of m l. This will make your answ er easier to study. 1.0 ml of alu m inum has m ass=___________ 1.0 ml of lead has mass=_______________

182

C oncep tu al In v en tio n . 7. Is th e m ass of 1 m l of any substance the sam e?

How is it different? Explain.

8. U sing th e new term inology state your findings about w ater, alum inum , and lead.

9. W rite an equation for density. (Hint: Use, D ensity=p)

10. W hat did you obtain as the density of the alum inum cylinder?

Of the lead object?

11. Find th e accepted value off density from a physics book. for lead accepted v alu es:______ for alum inum , a n d C alculate

% erro r = ____________ for alum inum % erro r =_________________ for lead

183

Expansion Problems. 12. ] f a substance bas a density of 2 g/cm^, w h at is th e m ass of 1 substance?

of the

13. Explain th is in everyday words. H int if 1 cm^ of a substance had a m ass of 2 g, should a 1 m^ volume of th e same substance be more m assive or less m assive?

C alculate the m ass of th e 1 m^ volume.

14. An cubical object ju s t floats w ithout sinking in a fluid of density 1.40 g/cm^. If a side of the cube is 1.0 cm long w hat is th e m ass of the cube?

184

Archimedes* Principle E quipm ent: Balance on rin g stand w ith rubber band, alum inum C}dinder w ith a string, overflow can, 250 ml plastic cup, w ater Introduction. Do you feel th e sam e, heavier, or lighter in a swim m ing pool? This investigation wiU teach you about objects' mass as m easured in a ir and as m easured in w ater. E ^ lo ra tio n . 1. Using th e balance w ith rubber band attachm ent, determ ine an d record th e mass of the alum inum cylinder. Draw a diagram to show how you did this. Mass of cylinder=_________________

2. Similarly, determ ine and record th e m ass of the alum inum cylinder w hen it is totally subm erged in w ater. Fill the overflow can w ith w ater so th a t it is approxim ately 2 cm below the spout. Now submerge the alum inum cylinder. Do not allow the cylinder to re st on th e bottom of the cup. W hy should you not allow this?

M ass of cylinder in w ater= 3. Place the plastic cup under th e spout. Fill th e overflow can w ith w ater u n til w ater stops pouring out of th e spout. Em pty th e plastic cup and place it under the spout. W hat do you th in k will happen if you pour an y m ore w ater into the can?

185

Using a graduated cylinder pour 20.0 ml of w ater into th e can and record your observations. M easure and record the volum e of w ater th a t poured out. Is this w hat you expected? W hy or why not?

State w hat w ill happen if you were to pour 50.0 m l of w ater into th e can. Do it and te s t your predictions.

In sum m ary, w hat does th e overflow can allow you to do?

4. Now refill th e overflow can until w ater stops pouring out. Carefully place the sam e dry alum inum cylinder in the overflow can. Allow it to rest on th e bottom of th e can. D escribe w hat happens.

Why did it happen? Is this w hat you predicted?

5. Now record the m ass of th e w ater th a t flowed out. Mass of w ater overflow____________________

186

C onceptual In v en tio n . 6. Was th ere a difference in th e m ass of the alum inum c}dinder when it w as m easured in th e a ir (#1) as opposed to the w ater (#2)?

7. If so, how g re a t w as th is difference in mass?

8. Why do you th in k th e re is a difference? In other w ords, w h at does the w ater do? D raw a diagram to show this.

9. How does th is difference in m ass compare w ith th e m ass of w ater th a t poured out of th e can? State your findings in words.

10. W hat does th e m ass of w ater th a t overflowed represent? (H int: W hy did it overflow?) Now re sta te your findings to incorporate th is relationship and the term buoyant force.

187

EaqM&nmon. 11. D escribe an e^>erim ent in w hich you could obtain th e volume of your body w hen in a bathtub.

12. D escribe an experim ent in w hich you could obtain th e buoyant force of your body when in a bathtub?

13. You buy a ring a t a garage sale. In order to determ ine w hether or no t it's gold you perform an e:q>eriment. Its m ass in the air is 3 g. Its m ass in w ater is 2.77 g. Calculate th e buoyant force?

U sing th is, calculate th e density of th e ring. Do you th in k the ring is gold?

188

S p ecific H eat in S o lid s In trodu ction . The stu d en t will be able to determ ine th e affect th a t h eat has on different m aterials in order to determ ine the specific h e a t capacity of different m aterials. E quipm ent:

alum inum cylinder graduated cylinder 400 m l beaker styrofoam cup

lead w eight scales therm om eter h o t p late

string

E xploration. In th is lab you will be heating m etal cylinders and th en transferring them to w ater in a styrofoam cup. F irst, we m u st discuss w hat things affect how long it takes som ething to cool off or w arm up. 1. Does th e am ount of m a tte r in an object affect how m uch heat th a t you m ust add to w arm it up it to a particular tem perature? ff so, how? Can you cite an exam ple from your personal experience?

2. Does how m uch you increase th e tem perature affect how much h eat th a t you m ust add?

If so, how? Can you cite an exam ple from your personal experience?

Thus far, you have discovered th a t th e quantity of h e a t depends upon the m ass of the object and th e tem perature change through which the m aterial m ust g o .

189

Now you will perform an experim ent. 1. Place a pyrex 400 m l beaker filled w ith about 300 ml of w ater on a bu rn er to begin heating w hile you prepare th e re st of th e fôqperiment. 2. Record the description and m aterial of each m etal object in th e d a ta table. 3. Record the m ass of each object (in gram s) in th e data table b en eath th e nam e of the substance. 4. A ttach a strin g about 30 cm long to each object. Place th e m etal object in th e beaker of hot w ater. D o n t allow th e strin g to touch th e h ea ter plate. 5. U sin g th e grad u ated C3d in d er, pour 300 g o f ta p w ater in to a styrofoam cup.

6. When the w ater has b ^ u n to boil, record th e tem perature of th e w ater as Tmi, b u t DONT leave th e therm om eter on th e bottom of th e beaker. 7. Why does th e tem perature of th e boiling w ater represent th e tem perature of the m etal initially?

8. Record the initial tem perature of th e w ater (as Twi) in the styrofoam cup ju s t before you are ready to tran sfer th e hot m etal cylinder into th e cup. Be sure th a t the m etal cylinder is in th e boiling w ater for a t least 3 m inutes before you transfer it. L ift th e cylinder off of the bottom of the beaker for 1 min. before you tran sfer it to th e cup. 9. T ransfer the hot m etal cylinder to th e w ater in th e styrofoam cup. S et the cup on the table and record th e tem perature o f the w ater in th e styrofoam cup un til it stops risin g and begins to fall again. Record th is tem perature as Twf and as Tmf. 10. W hat is the final tem perature of the m etal object now? Why? 11. Repeat the experim ent (steps 5,6, and 8) for th e other cylinder and record th e data in the d ata table.

190

Data Table materi^ mass in g

Tmetaljuüti^XjC) Tmetal final (C) IChange in temp, of metal i mass X chg. in temp_____ material mass in g Twater initially (C) Twater final (C) IChange in temp, of water i mass X chg. in temp. _

water

1 ____water........... ' !i .......................... 1

1

C onceptual In ven tion . 10. Calculate m ass tim es the change in tem perature for both th e m etal and w ater and record above.

11. When you p u t th e hot m etal cylinder into th e cooler water, w h at happens?

12. Should the h e a t lost by th e m etal cylinder equal the h eat gained by th e w ater?

Why?

191

13. E arlier we reasoned th a t the am ount of heat depends on m an d the change in T. Is the m AT of the w ater equal to th e m AT of the metal?

W hat is your evidence?

14. W hat could be th e other factor th a t makes the m AT's different?

192

15. How could you make the m AT's equal (to take this into account)?

Could you multiply by some num ber to m ake them equal?

16. Let this number be c. Now if h eat is equal to Q, then write an expression for the heat.

193

17. Call c the specific h e a t capacity. For convenience let c for w ater be 1 cal/g oc. Since we earlier determined th a t the heat lost by th e m etal should equal the h ea t gained by th e water, then calculate th e specific h e a t capacity for each of th e m etals th a t you used.

18. The specific h e a t capacity is a constant th a t depends on Eiqwrnamon. Complete the problems in th e text on heat.

194

APPENDIX D: M eaningful Verbal Reception Learning Concept Maps Figure 1: Energy Figure 2: Energy and M a tter Figure 3: Thermal E i^an sio n , Heat and Thermometers Figure 4: Student Map on H eat Figure 5: Student Map on H eat Figured: Newton’s Laws Figure 7: Energy Methods (No Friction) Figure 8: Enerçy M ethods (Friction) Figure 9: Energy, M atter, Energy, D ensity Figure 10: Student M ap on M atter Figure 11: Student M ap on Energy, M atter, Density, P ressure Figure 12: Archimedes’ Principle Figure 13: Falling Objects

195

c

WCKK/Zx*w**

âm vH cnoM

c e/gAAe^y

4S

Figure 1. E nergy was considered to be one of the m ost general topics in physics. This concept m ap roughly guided th e course of study for the meaningful verbal reception learning treatm ent.

196

War# £per4-iti may ftwwoH;

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^uH.af VoC ^ pLwJd jjf p k c f d

Figure 2. Energy and matter were chosen as the two most general topics in physics. This concept map connects at the upper left to Figure 1. This map as well as the previous one guided presentation of the material in the course for the MVRL students.

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Ct*0^ (C «T It yTo*caJ « \ jme^SY^

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Figure 4. S tudent constructed concept m ap (sim ilar to th a t of researcher in Figure 3) th a t w as considered to be fairly well constructed.

199

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r#*J CoM^ 4riar
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Figures. Student constructed concept map similar to Figures 3 an d 4 although this one has much fewer linkages.

200

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Y T> u  w iü  in -the Figures. Concept m ap drawn during class discussion about solving Newton’s Law problems (drawn here by researcher). After heat and energy topics, motion was introduced in the MVRL treatm ent as motion was considered to be a more specific item th an heat/energy. 201

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Figyre 7 8. This concept map drawn after students read about energy ^ h m q u e s for motion (w ith (8) and without (7) friction) problem solving and drew their own concept m aps over the sections in th e textbook. This m ap was drawn during class discussion of the material. 202

P«9C^(

Rjw.l» i« rmmumtnm» ^,^omn••r*^m* T» «••**'

a - v s 5 - t s / (g :q ? 5 D w o.oiKi«FfV)

Fiyure9. S tudents were to read a section on energy, m atter, pressure, and density to draw a concept map relating these item s. This was a concept map th a t resulted from class discussion afterward.

203

crn>^

r hf^*K V»(***«. ) «o

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Figure 10. Student concept map with very few linkages to m atter, no links to density or pressure.

204

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Figure 11. Students were to read a section on energy, matter, pressure, and density and to draw a concept map relating those items. This was one of the better student maps.

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Figure 12. Concept map th a t resulted from discussion over tex t reading on Archimedes’ Principle. S tudents read th e sections assigned and constructed their own maps. This m ap w as used in lab also.

206

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Figure 13. Concept m ap on th e topic of the physics of falling objects. This was constructed by th e class after reading Ihe text on the topic and constructing th eir own concept maps.

207

APPENDIX E: Miscellaneous Statistics ANCOVA Adjusted M eans Pearson Correlation M atrix for Force D ata Pearson Correlation M atrix for Density/Archimedes’ Principle Data Pearson Correlation M atrix for H eat D ata Descriptive Statistics Forces Data Descriptive Statistics Density/Archimedes’ Principle D ata Descriptive Statistics H eat Data

208

Table 10: ANCOVA Adjusted Means

to o

to

T able P o s tte s t M ean Scores LC MVRL LC R aw MVRL R aw * * 1 Overall force understanding 58.511 47.649 2 Overall density understanding 34.450 27.425 33.667 28.208 3 Overall heat understanding 39.960 44.207 39.917 44.250 4 Learning approach (force) 65.773 66.707 65.280 67.200 5 Learning approach (density) 65.346 65.737 64.875 66.208 6 Learning approach (heat) 68.098 65.402 68.333 65.167 7 Force Concept Understanding 13.358 12.522 12.840 13.040 7 Force Problem Understanding 3.344 2.456 3.280 2.520 7 Force Mental Model Understanding 42.251 32.229 42.360 32.120 8 Density/ Archimedes' Concept Understanding 10.273 9.061 10.167 9.167 8 Density/Archimedes' Problem Understanding 4.079 2.587 3.833 2.833 8 Density/Archimedes' Mental Model Understanding | 19.913 15.962 19.667 16.208 9 Heat Concept Understanding 8.442 8.558i 8.375 8.625 9 Heat Problem Understanding 1.764 2.736 1.750 2.750 9 Heat Mental Model Understanding 29.417 33.249 29.792 32.875 Note: LC = means for learning cycle treatment (adjusted) LC Raw = raw m eans for learning cycle treatm ent MVRL = means for meaningful verbal reception learning treatm ent (adjusted) MVRL Raw = raw means for meaningful verbal reception learning treatment * = mean adjustm ent not necessary (ANOVA = ANCOVA)

Table 11. Pearson Corrélation Matrix for Force Data FCl FPl FMI RAl LAI FM Ul TX FC2 FP2 FM2 FMU2

FCl 1.000 .133 .104 .211 .195 .529 .239 .587 -.020 - .376 - .278

TX FC2 FP2 FM2 FMU2

TX 1.000 .031 -.213 - .254 -.263

FPl 1.000 .322 .357 .154 .372 .288 .131 .087 .053 .024 FC2 1.000 .354 .132 .060

FM I 1.000 -.075 .249 .898 .073 .002 .157 .088 .100

RA l

1.000 .310 .045 .085 .451 .391 -.106 .002

LAI

1.000 .300 .139 .191 .073 -.090 -.052

FP2

FM2

FMU2

1.000 .208 .347

1.000 .979

1.000

Number of observations: 50 Definition of Variables: F C l = force concept understanding pretest F P l = force problem solving pretest FMI =force mental model pretest RAI =reasoning ability p retest LAI = learning orientation pretest FMU1= overall meaningful understanding pretest TX = treatm ent (1 = LC, 2 = MVRL) FC2 = force concept posttest FP2 = force problem solving posttest FM2 = force mental model posttest FMU2 = force meaningful understanding overall posttest

210

FM U l

1.000 .178 .263 .127 -.093 -.038

Table 12. Pearson Correlation Matrix for Density/Archimedes’ Principle Data D Cl D PI DM1 RAl LAI DMUl TX DC2 DP2 DM2 DMU2

DCl 1.000 .230 -.053 .226 .280 .564 .016 .406 .157 .193 .287

TX DC2 DP2 DM2 DMU2

TX 1.000 -.155 -.277 -.141 -.198

D PI 1.000 .300 .242 .445 .509 .410 -.033 .233 -.254 -.203

DM1

RAl

1.000 .109 .143 .784 .268 .032 -.117 .024 .014

1.000 .324 .248 .071 .387 .199 .034 .147

DC2

DP2

DM2

1.000 .441 .201 .471

1.000 .090 .315

1.000 .951

LAI

DMUl

1.000 .335 .061 .284 .344 .052 .158 DMU2

1.000

Number of observations: 48 Definition of Variables: D Cl = density concept understanding pretest D PI = density problem solving pretest DM1 = density m ental model p retest RAl = reasoning ability pretest LAI = learning orientation pretest DMU1= density meaningful understanding overall pretest TX = treatm ent (1 = LC, 2 = MVRL) DC2 = density concept posttest DP2 = density problem solving posttest DM2 = density m ental model posttest DMU2 = density meaningful understanding overall posttest

211

1.000 .276 .252 .034 .091 .145

Table 13: Pearson Correlation Matrix for Heat Data HCl H Pl HMl RAl LAI HM Ul TX HC2 HP2 HM2 HMU2

HCl 1.000 .300 .341 .451 .148 .577 .053 .243 .153 .055 .107

HM Ul TX HC2 HP2 HM2 HMU2

HM U l 1.000 .318 .266 .166 .022 .040

H Pl

HMl

RA l

LAI

1.000 .149 .012 .963 .359 .211 .136 -.030 .021

1.000 .365 .263 .064 .348 .356 -.135 -.032

1.000 .060 .029 .308 .190 .092 .157

TK

HC2

HP2

1.000 .049 .338 .109 .143

1.000 .584 .116 .334

1.000 .206 .389

1.000 .202 .280 .207 .305 .112 .393 .151 -.213 -.117

HM2

HMU2

1.000 .972

Number of observations: 48 Definition of Variables: H C l = heat concept understanding pretest H P l = heat problem solving pretest H M l = heat m ental model pretest HM Ul = h eat meaningful understanding overall pretest RAl = reasoning ability pretest LAI = learning orientation pretest TX = treatm ent (1 = LC, 2 = MVRL) HC2 = heat concept posttest HP2 = heat problem solving posttest HM2 = heat mental model posttest HMU2 = heat meaningful understanding overall posttest

212

1.000

Table 14: Descriptive Statistics for Forces Data ForLC (TX == 1) with total observations:

25

FCl MINIMUM 3.000 MAXIMUM 16.000 MEAN 7.760 VARIANCE 11.857 STANDARD DEV 3.443

FPl .000 1.000 .040 .040 .200

FM I .000 22.000 5.120 30.443 5.518

RA I 2.000 10.000 6.800 4.833 2.198

LAI 55.000 85.000 65.240 60.690 7.790

FM U l 4.000 31.000 12.920 45.743 6.763

FC2 7.000 20.000 12.840 12.807 3.579

FP2 1.000 6.000 3.280 2.210 1.487

FM2 11.000 85.000 42.360 403.657 20.091

FMU2 29.000 102.000 58.480 389.093 19.725

MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

For MVRL (TX = 2) with total observations: MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

FC l 5.000 17.000 9.400 11.250 3.354

FPl 000 1.000 .240 .190 .436

FM I .000 32.000 6-080 59.660 7.724

25 RA I 3.000 10.000 7.160 4.473 2.115

LA I 51.000 80.000 67.320 53.977 7.347

FM U l

FC2

FP2

FM2

FMU2

6.000 44.000 15.720 79.043 8.891

8.000 19.000 13.040 9.290 3.048

.000 6.000 2.520 4.093 2.023

6.000 75.000 32.120 388.943 19.722

21.000 92.000 47.680 429.727 20.730

Note: Refer to Table 11 for variable definitions

213

Table 15. Descriptive Statistics for Density/Archimedes’ Principle Data For LC (TX = 1) with total observations:

24

MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

DCl 2.000 11.000 6.375 8.853 2.975

D PI .000 1.000 .083 .080 .282

DM1 .000 7.000 1.458 4.346 2.085

RAl 1.000 10.000 6.917 7.993 2.827

LAI 58.000 77.000 65.625 30.245 5.500

MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

DM Ul 2.000 14.000 7.917 13.297 3.647

DC2 5.000 15.000 10.167 9.362 3.060

DP2 1.000 6.000 3.833 2.580 1.606

DM2 2.000 48.000 19.667 140.406 11.849

DMU2 13.000 60.000 33.667 146.406 12.100

For MVRL (TX = 2) w ith total observations:

24

DCl MINIMUM 3.000 MAXIMUM 11.000 6.458 MEAN VARIANCE 5.129 STANDARD DEV 2.265

DPI .000 2.000 .625 .679 .824

DM1 .000 20.000 3.333 19.275 4.390

RAl 1.000 10.000 7.292 6.389 2.528

LA I 53.000 83.000 66.458 66.259 8.140

DM Ul 4.000 27.000 10.417 26.341 DEV 5.132

DC2 2.000 15.000 9.167 11.797 3.435

DP2 .000 6.000 2.833 3.710 1.926

DM2 2.000 59.000 16.208 168.781 12.992

DMU2 13.000 80.000 28.208 234.346 15.308

MINIMUM MAXIMUM MEAN VARIANCE STANDARD

Note: Refer to Table 12 for variable definitions •

214

Table 16. Descriptive Statistics for Heat Data ForL C (TX = 1) with total observations: HCl MINIMUM 2.000 MAXIMUM 11.000 MEAN 6.208 VARIANCE 4.868 STANDARD DEV 2.206 MINIMUM MAXIMUM MEAN VARIANCE STANDARD

HM Ul 2.000 38.000 13.542 67.389 DEV 8.209

H Pl .000 1.000 .208 .172 .415

24

HMl .000 27.000 7.125 44.462 6.668

HC2 4.000 13.000 8.375 6.418 2.533

HP2 .000 4.000 1.750 1.587 1.260

For MVRL (TX = 2) with total observations: HCl 3.000 10.000 6.417 3.123 1.767

H Pl .000 1.000 .125 .114 .338

HMl .000 21.000 11.667 28.232 5.313

HM Ul MINIMUM 8.000 29.000 MAXIMUM 18.208 MEAN 33.563 VARIANCE STANDARD DEV 5.793

HC2 4.000 14.000 8.625 7.201 2.683

HP2 .000 5.000 2.750 2.457 1.567

MINIMUM MAXIMUM MEAN VARIANCE STANDARD DEV

Note: Refer to Table 13 for variable definitions

215

RA l 1.000 10.000 6.958 7.607 2.758

LAI 52.000 75.000 64.750 29.587 5.439

HM2 14.000 55.000 29.792 142.085 11.920

HMU2 20.000 66.000 39.917 152.341 12.343

24 RAl 1.000 10.000 7.292 6.389 2.528

LAI 38.000 83.000 65.208 99.737 9.987

HM2 HMU2 8.000 20.000 61.000 77.000 44.250 32.875 266.810 314.457 16.334 17.733 •

IMAGE EVALUATION TEST TARGET ( Q A - 3 )

1.0

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2.0

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1.6

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